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Journal articles on the topic 'Dynamical hypothesis'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

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1

Chater, Nick, and Ulrike Hahn. "What is the dynamical hypothesis?" Behavioral and Brain Sciences 21, no. 5 (October 1998): 633–34. http://dx.doi.org/10.1017/s0140525x98271731.

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Van Gelder's specification of the dynamical hypothesis does not improve on previous notions. All three key attributes of dynamical systems apply to Turing machines and are hence too general. However, when a more restricted definition of a dynamical system is adopted, it becomes clear that the dynamical hypothesis is too underspecified to constitute an interesting cognitive claim.

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2

Bonelli, A., and M. Rasetti. "Riemann hypothesis and dynamical systems." Le Journal de Physique IV 08, PR6 (October 1998): Pr6–189—Pr6–195. http://dx.doi.org/10.1051/jp4:1998625.

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3

van Gelder, Tim. "The dynamical hypothesis in cognitive science." Behavioral and Brain Sciences 21, no. 5 (October 1998): 615–28. http://dx.doi.org/10.1017/s0140525x98001733.

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According to the dominant computational approach in cognitive science, cognitive agents are digital computers; according to the alternative approach, they are dynamical systems. This target article attempts to articulate and support the dynamical hypothesis. The dynamical hypothesis has two major components: the nature hypothesis (cognitive agents are dynamical systems) and the knowledge hypothesis (cognitive agents can be understood dynamically). A wide range of objections to this hypothesis can be rebutted. The conclusion is that cognitive systems may well be dynamical systems, and only sustained empirical research in cognitive science will determine the extent to which that is true.

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4

Eiser, J. Richard. "The dynamical hypothesis in social cognition." Behavioral and Brain Sciences 21, no. 5 (October 1998): 638. http://dx.doi.org/10.1017/s0140525x98331738.

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Research in attitudes and social cognition exemplifies van Gelder's distinction between the computational and dynamical approaches. The former emphasizes linear measurement and rational decision-making. The latter considers processes of associative memory and self-organization in attitude formation and social influence. The study of dynamical processes in social cognition has been facilitated by connectionist approaches to computation.

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5

French, Robert M., and Elizabeth Thomas. "The dynamical hypothesis: One battle behind." Behavioral and Brain Sciences 21, no. 5 (October 1998): 640–41. http://dx.doi.org/10.1017/s0140525x98361737.

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What new implications does the dynamical hypothesis have for cognitive science? The short answer is: none. The target article is basically an attack on traditional symbolic artificial intelligence (AI) and differs very little from prior connectionist criticisms of it. For the past 10 years, the connectionist community has been well aware of the necessity of using (and understanding) dynamically evolving, recurrent network models of cognition.

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6

Loh, Marco, Edmund T. Rolls, and Gustavo Deco. "A Dynamical Systems Hypothesis of Schizophrenia." PLoS Computational Biology 3, no. 11 (November 9, 2007): e228. http://dx.doi.org/10.1371/journal.pcbi.0030228.

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7

Vácha, Lukáš, and Miloslav S. Vošvrda. "Dynamical Agents' Strategies and the Fractal Market Hypothesis." Prague Economic Papers 14, no. 2 (January 1, 2005): 163–70. http://dx.doi.org/10.18267/j.pep.260.

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8

Petitot, Jean. "Dynamical modeling and morphological analysis." Behavioral and Brain Sciences 21, no. 5 (October 1998): 649. http://dx.doi.org/10.1017/s0140525x98461739.

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After a historical sketch of the dynamical hypothesis, we stress that it is a functionalist hypothesis. We then tackle the point of a dynamical approach to constituent structures and emphasize that dynamical modeling must be coupled with morphological analysis.

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9

Garson, James W. "Why dynamical implementation matters." Behavioral and Brain Sciences 21, no. 5 (October 1998): 641–42. http://dx.doi.org/10.1017/s0140525x98371733.

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Another objection to the dynamical hypothesis is explored. To resolve it completely, one must focus more directly on an area not emphasized in van Gelder's discussion: the contributions of dynamical systems theory to understanding how cognition is neutrally implemented.

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10

Braisby, Nick, Richard Cooper, and Bradley Franks. "Why the dynamical hypothesis cannot qualify as a law of qualitative structure." Behavioral and Brain Sciences 21, no. 5 (October 1998): 630–31. http://dx.doi.org/10.1017/s0140525x98241732.

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Van Gelder presents the dynamical hypothesis as a novel law of qualitative structure to compete with Newell and Simon's (1976) physical symbol systems hypothesis. Unlike Newell and Simon's hypothesis, the dynamical hypothesis fails to provide necessary and sufficient conditions for cognition. Furthermore, imprecision in the statement of the dynamical hypothesis renders it unfalsifiable.

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11

Horgan, Terence, and John Tienson. "Resisting the tyranny of terminology: The general dynamical hypothesis in cognitive science." Behavioral and Brain Sciences 21, no. 5 (October 1998): 643. http://dx.doi.org/10.1017/s0140525x98391736.

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What van Gelder calls the dynamical hypothesis is only a special case of what we here dub the general dynamical hypothesis. His terminology makes it easy to overlook important alternative dynamical approaches in cognitive science. Connectionist models typically conform to the general dynamical hypothesis, but not to van Gelder's.

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12

Davids, Keith, and Simon Bennett. "The dynamical hypothesis: The role of biological constraints on cognition." Behavioral and Brain Sciences 21, no. 5 (October 1998): 636. http://dx.doi.org/10.1017/s0140525x98301739.

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For the dynamical hypothesis to be defended as a viable alternative to a computational perspective on natural cognition, the role of biological constraints needs to be considered. This task requires a detailed understanding of the structural organization and function of the dynamic nervous system, as well as a theoretical approach that grounds cognitive activity within the constraints of organism and ecological context.

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13

Shaw, Robert, and Jeffrey Kinsella-Shaw. "Could Optical ‘Pushes’ Be Inertial Forces? A Geometro-Dynamical Hypothesis." Ecological Psychology 19, no. 3 (June 29, 2007): 305–20. http://dx.doi.org/10.1080/10407410701432352.

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14

Noelle, David C. "Is the dynamical hypothesis falsifiable? On unification in theories of cognition." Behavioral and Brain Sciences 21, no. 5 (October 1998): 647–48. http://dx.doi.org/10.1017/s0140525x98441736.

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The dynamical hypothesis is strong in that, for it to be true, every cognitive phenomenon must be best modeled by a dynamical system. Depending on how it is interpreted, however, the hypothesis may be seen as probably false or even unfalsifiable. Strengthening the hypothesis to require unification, or at least coherence, across models in different cognitive domains alleviates this problem.

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15

RUET, PAUL. "Local cycles and dynamical properties of Boolean networks." Mathematical Structures in Computer Science 26, no. 4 (November 20, 2014): 702–18. http://dx.doi.org/10.1017/s096012951400036x.

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We investigate the relationships between the dynamical properties of Boolean networks and properties of their Jacobian matrices, in particular the existence of local cycles in the associated interaction graphs. We define the notion of hereditarily bijective maps, and we use it to strengthen the property of unicity of a fixed point and to provide simplified proofs and generalizations of theorems relating attractors to the existence of local cycles, in particular local positive cycles. We then argue that this notion may not suffice to prove, under a suitable hypothesis such as the existence of a cyclic attractor or a stronger hypothesis, the existence of local negative cycles. We then consider a class of Boolean networks called and-or-nets, and for this class, we prove that the hypothesis of an antipodal attractive cycle implies the existence of a local negative cycle.

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16

Olsson, Mats H. M., William W. Parson, and Arieh Warshel. "Dynamical Contributions to Enzyme Catalysis: Critical Tests of A Popular Hypothesis." Chemical Reviews 106, no. 5 (May 2006): 1737–56. http://dx.doi.org/10.1021/cr040427e.

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17

Guesnerie, Roger. "Theoretical tests of the rational expectations hypothesis in economic dynamical models." Journal of Economic Dynamics and Control 17, no. 5-6 (September 1993): 847–64. http://dx.doi.org/10.1016/0165-1889(93)90018-n.

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18

Chrisley, Ronald L. "What might dynamical intentionality be, if not computation?" Behavioral and Brain Sciences 21, no. 5 (October 1998): 634–35. http://dx.doi.org/10.1017/s0140525x98281738.

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(1) Van Gelder's concession that the dynamical hypothesis is not in opposition to computation in general does not agree well with his anticomputational stance. (2) There are problems with the claim that dynamic systems allow for nonrepresentational aspects of computation in a way in which digital computation cannot. (3) There are two senses of the “cognition is computation” claim and van Gelder argues against only one of them. (4) Dynamical systems as characterized in the target article share problems of universal realizability with formal notions of computation, but differ in that there is no solution available for them. (5) The dynamical hypothesis cannot tell us what cognition is, because instantiating a particular dynamical system is neither necessary nor sufficient for being a cognitive agent.

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19

O'Brien, Gerard. "Digital computers versus dynamical systems: A conflation of distinctions." Behavioral and Brain Sciences 21, no. 5 (October 1998): 648–49. http://dx.doi.org/10.1017/s0140525x98451732.

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The distinction at the heart of van Gelder's target article is one between digital computers and dynamical systems, but this distinction conflates two more fundamental distinctions in cognitive science that should be kept apart. When this conflation is undone, it becomes apparent that the computational hypothesis is not as dominant in contemporary cognitive science as van Gelder contends; nor has the dynamical hypothesis been neglected.

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20

Pavlos, G. P., D. Kugiumtzis, M. A. Athanasiu, N. Hatzigeorgiu, D. Diamantidis, and E. T. Sarris. "Nonlinear analysis of magnetospheric data Part II. Dynamical characteristics of the AE index time series and comparison with nonlinear surrogate data." Nonlinear Processes in Geophysics 6, no. 2 (June 30, 1999): 79–98. http://dx.doi.org/10.5194/npg-6-79-1999.

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Abstract. In this study we have used dynamical characteristies such as Lyapunov exponents, nonlinear dynamic models and mutual information for the nonlinear analysis of the magnetospheric AE index time series. Similarly with the geometrical characteristic studied in Pavlos et al. (1999b), we have found significant differences between the original time series and its surrogate data. These results also suggest the rejection of the null hypothesis that the AE index belongs to the family of stochastic linear signals undergoing a static nonlinear distortion. Finally, we believe that these results support the hypothesis of nonlinearity and chaos for the magnetospheric dynamics.

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21

Xia, Xin Tao. "Hypothesis of Rolling Bearing Performance Evolvement." Advanced Materials Research 488-489 (March 2012): 1087–93. http://dx.doi.org/10.4028/www.scientific.net/amr.488-489.1087.

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Poor information means that characteristic information presented in the subject investigated is incomplete and insufficient, with a small sample and the lack in prior knowledge of probability distributions and trends. For a long time, experiments on the rolling bearing performance concern primarily with statistical evaluation of the fatigue life. With the development of aeronautic and astronautic undertakings, new requirements for the variability of the bearing performance, such as friction, wear, vibration, and temperature rise, are driven. Because the number of characteristic data is small and prior information on probability distributions and trends is poor, statistics has difficulty in assessing the bearing performance. How can the problem be solved? There is a phenomenon in Nature, i.e., genetic variations of a species are likely to result in some strange change. Inspired by this, the paper advanced a hypothesis, viz., maybe some genetic variation drive the nonlinearly dynamical evolvement of the information poor process of the bearing performance. To demonstrate this hypothesis, the paper found the variant gene, presented the concept of the poor information equivalence relation, and proposed the method for construction of the information poor space to reveal the new properties of the nonlinearly dynamical evolvement of the modern bearing performance.

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22

Jafari, Sajad, Fahimeh Nazarimehr, J. C. Sprott, and Seyed Mohammad Reza Hashemi Golpayegani. "Limitation of Perpetual Points for Confirming Conservation in Dynamical Systems." International Journal of Bifurcation and Chaos 25, no. 13 (December 15, 2015): 1550182. http://dx.doi.org/10.1142/s0218127415501825.

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Perpetual Points (PPs) have been introduced as an interesting new topic in nonlinear dynamics, and there is a hypothesis that these points can determine whether a system is dissipative or not. This paper demonstrates that this hypothesis is not true since there are counterexamples. Furthermore, we explain that it is impossible to determine dissipation of a system based only on the structure of the system and its equations.

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23

Rabhi, Anissa. "On Threshold Choice in Hypothesis Testing for Dynamical Systems with Small Noise." Communications in Statistics - Theory and Methods 42, no. 5 (March 2013): 800–811. http://dx.doi.org/10.1080/03610926.2011.579374.

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24

BENTZEN, N. C. K., A. M. ZHABOTINSKY, and J. L. LAUGESEN. "MODELING OF GLUTAMATE-INDUCED DYNAMICAL PATTERNS." International Journal of Neural Systems 19, no. 06 (December 2009): 395–407. http://dx.doi.org/10.1142/s0129065709002105.

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Based on established physiological mechanisms, the paper presents a detailed computer model, which supports the hypothesis that temporal lobe epilepsy may be caused by failure of glutamate reuptake from the extracellular space. The elevated glutamate concentration causes an increased activation of NMDA receptors in pyramidal neurons, which in turn leads to neuronal dynamics that is qualitatively identical to epileptiform activity. We identify by chaos analysis a surprising possibility that muscarinergic receptors can help the system out of a chaotic regime.

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25

Mishra, Ashish, and Mukul Kumar. "Solar Dynamical Processes II." Advanced Journal of Graduate Research 6, no. 1 (February 11, 2019): 1–13. http://dx.doi.org/10.21467/ajgr.6.1.1-13.

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The present article is the successor of Solar Dynamical Processes I. The previous article was focused on the Sun, its magnetic field with an emphasis on various dynamical processes occurring on the Sun, e.g. sunspots, prominence and bright points which in turn plays a fundamental role in regulating the space weather. This article is emphasized on the solar dynamical processes and develop an extensive understanding of the various phenomena involved in their origin. The article also covers various models and hypothesis put forward by pioneer scientists on the basis of their observation by space-borne and ground-based instruments. This article shade light over a wide range of dynamical processes e.g., solar flares, coronal mass ejections, solar jets and coronal holes. Solar jets, the small-scale transient activities are found to have association with the other transient activities (e.g., mini-flares and mini-filaments). Flares as well as the coronal mass ejections are responsible for releasing a large amount of high energy charged particles and magnetic flux into the interplanetary space, and are being considered as the main drivers of space weather.

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26

Bernard, Patrick. "The Lax–Oleinik semi-group: a Hamiltonian point of view." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 142, no. 6 (November 27, 2012): 1131–77. http://dx.doi.org/10.1017/s0308210511000059.

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The weak KAM theory was developed by Fathi in order to study the dynamics of convex Hamiltonian systems. It somehow makes a bridge between viscosity solutions of the Hamilton–Jacobi equation and Mather invariant sets of Hamiltonian systems, although this was fully understood only a posteriori. These theories converge under the hypothesis of convexity, and the richness of applications mostly comes from this remarkable convergence. In this paper, we provide an elementary exposition of some of the basic concepts of weak KAM theory. In a companion paper, Albert Fathi exposed the aspects of his theory which are more directly related to viscosity solutions. Here, on the contrary, we focus on dynamical applications, even if we also discuss some viscosity aspects to underline the connections with Fathi's lecture. The fundamental reference on weak KAM theory is the still unpublished book Weak KAM theorem in Lagrangian dynamics by Albert Fathi. Although we do not offer new results, our exposition is original in several aspects. We only work with the Hamiltonian and do not rely on the Lagrangian, even if some proofs are directly inspired by the classical Lagrangian proofs. This approach is made easier by the choice of a somewhat specific setting. We work on ℝd and make uniform hypotheses on the Hamiltonian. This allows us to replace some compactness arguments by explicit estimates. For the most interesting dynamical applications, however, the compactness of the configuration space remains a useful hypothesis and we retrieve it by considering periodic (in space) Hamiltonians. Our exposition is centred on the Cauchy problem for the Hamilton–Jacobi equation and the Lax–Oleinik evolution operators associated to it. Dynamical applications are reached by considering fixed points of these evolution operators, the weak KAM solutions. The evolution operators can also be used for their regularizing properties; this opens an alternative route to dynamical applications.

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27

Recchi, Simone. "Dynamical and Chemical Evolution of IZw18." Publications of the Astronomical Society of Australia 21, no. 2 (2004): 157–60. http://dx.doi.org/10.1071/as03065.

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AbstractWe study the effect of different star formation regimes on the dynamical and chemical evolution of IZw18, the most metal-poor dwarf galaxy locally known. To do that we adopt a two-dimensional hydrocode coupled with detailed chemical yields originating from Type II and Type Ia supernovae and from intermediate-mass stars. Particular emphasis is devoted to the problem of mixing of metals. We conclude that, under particular conditions, cooling of metals occurs with a timescale of the order of 10 Myr, thus confirming the hypothesis of instantaneous mixing adopted in chemical evolution models. We try to draw conclusions about the star formation history and the age of the last burst in IZw18.

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28

Fujii, Hiroshi, Hiroyuki Ito, Kazuyuki Aihara, Natsuhiro Ichinose, and Minoru Tsukada. "Dynamical Cell Assembly Hypothesis — Theoretical Possibility of Spatio-temporal Coding in the Cortex." Neural Networks 9, no. 8 (November 1996): 1303–50. http://dx.doi.org/10.1016/s0893-6080(96)00054-8.

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29

Beloglazov, I. N., and S. N. Kazarin. "Optimal Algorithms of the Nonlinear Filtering, Identification and Hypothesis Checking for Dynamical Systems." IFAC Proceedings Volumes 34, no. 6 (July 2001): 651–56. http://dx.doi.org/10.1016/s1474-6670(17)35252-7.

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30

Kowalski, Krzysztof. "A hypothesis concerning ‘quantal’ Hilbert space criterion of chaos in nonlinear dynamical systems." Chaos, Solitons & Fractals 7, no. 5 (May 1996): 653–57. http://dx.doi.org/10.1016/0960-0779(94)00213-4.

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31

Qu, Zhilin. "Critical mass hypothesis revisited: role of dynamical wave stability in spontaneous termination of cardiac fibrillation." American Journal of Physiology-Heart and Circulatory Physiology 290, no. 1 (January 2006): H255—H263. http://dx.doi.org/10.1152/ajpheart.00668.2005.

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The tendency of atrial or ventricular fibrillation to terminate spontaneously in finite-sized tissue is known as the critical mass hypothesis. Previous studies have shown that dynamical instabilities play an important role in creating new wave breaks that maintain cardiac fibrillation, but its role in self-termination, in relation to tissue size and geometry, is not well understood. This study used computer simulations of two- and three-dimensional tissue models to investigate qualitatively how, in relation to tissue size and geometry, dynamical instability affects the spontaneous termination of cardiac fibrillation. The major findings are as follows: 1) Dynamical instability promotes wave breaks, maintaining fibrillation, but it also causes the waves to extinguish, facilitating spontaneous termination of fibrillation. The latter effect predominates as dynamical instability increases, so that fibrillation is more likely to self-terminate in a finite-sized tissue. 2) In two-dimensional tissue, the average duration of fibrillation increases exponentially as tissue area increases. In three-dimensional tissue, the average duration of fibrillation decreases initially as tissue thickness increases as a result of thickness-induced instability but then increases after a critical thickness is reached. Therefore, in addition to tissue mass and geometry, dynamical instability is an important factor influencing the maintenance of cardiac fibrillation.

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32

Villani, Marco, Luca La Rocca, Stuart Alan Kauffman, and Roberto Serra. "Dynamical Criticality in Gene Regulatory Networks." Complexity 2018 (October 4, 2018): 1–14. http://dx.doi.org/10.1155/2018/5980636.

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A well-known hypothesis, with far-reaching implications, is that biological evolution should preferentially lead to states that are dynamically critical. In previous papers, we showed that a well-known model of genetic regulatory networks, namely, that of random Boolean networks, allows one to study in depth the relationship between the dynamical regime of a living being’s gene network and its response to permanent perturbations. In this paper, we analyze a huge set of new experimental data on single gene knockouts in S. cerevisiae, laying down a statistical framework to determine its dynamical regime. We find that the S. cerevisiae network appears to be slightly ordered, but close to the critical region. Since our analysis relies on dichotomizing continuous data, we carefully consider the issue of an optimal threshold choice.

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33

Tsuda, Ichiro. "Toward an interpretation of dynamic neural activity in terms of chaotic dynamical systems." Behavioral and Brain Sciences 24, no. 5 (October 2001): 793–810. http://dx.doi.org/10.1017/s0140525x01000097.

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Using the concepts of chaotic dynamical systems, we present an interpretation of dynamic neural activity found in cortical and subcortical areas. The discovery of chaotic itinerancy in high-dimensional dynamical systems with and without a noise term has motivated a new interpretation of this dynamic neural activity, cast in terms of the high-dimensional transitory dynamics among “exotic” attractors. This interpretation is quite different from the conventional one, cast in terms of simple behavior on low-dimensional attractors. Skarda and Freeman (1987) presented evidence in support of the conclusion that animals cannot memorize odor without chaotic activity of neuron populations. Following their work, we study the role of chaotic dynamics in biological information processing, perception, and memory. We propose a new coding scheme of information in chaos-driven contracting systems we refer to as Cantor coding. Since these systems are found in the hippocampal formation and also in the olfactory system, the proposed coding scheme should be of biological significance. Based on these intensive studies, a hypothesis regarding the formation of episodic memory is given.

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34

Sempf, Mario, Klaus Dethloff, Dörthe Handorf, and Michael V. Kurgansky. "Toward Understanding the Dynamical Origin of Atmospheric Regime Behavior in a Baroclinic Model." Journal of the Atmospheric Sciences 64, no. 3 (March 1, 2007): 887–904. http://dx.doi.org/10.1175/jas3862.1.

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Abstract Dynamical mechanisms of atmospheric regime behavior are investigated in the context of a quasigeostrophic three-level T21 model of the wintertime atmospheric circulation over the Northern Hemisphere. The model, driven by realistic orography and using a thermal forcing determined by a newly developed tuning procedure, is shown to possess a reasonable climatology and to simulate the Arctic Oscillation quite realistically. It exhibits pronounced internally generated interannual and decadal variability and, in particular, circulation regimes that agree fairly well with observed ones. Two known hypotheses about the origin of regime behavior, as it occurs in the model herein are addressed: (i) multiple equilibria and (ii) chaotic itinerancy between attractor ruins. The first hypothesis is falsified at very high probability, while the second is likely to be true.

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35

LUO, XIAODONG, MICHAEL SMALL, MARIUS-F. DANCA, and GUANRONG CHEN. "ON A DYNAMICAL SYSTEM WITH MULTIPLE CHAOTIC ATTRACTORS." International Journal of Bifurcation and Chaos 17, no. 09 (September 2007): 3235–51. http://dx.doi.org/10.1142/s0218127407018993.

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The chaotic behavior of the Rabinovich–Fabrikant system, a model with multiple topologically different chaotic attractors, is analyzed. Because of the complexity of this system, analytical and numerical studies of the system are very difficult tasks. Following the investigation of this system carried out in [Danca & Chen, 2004], this paper verifies the presence of multiple chaotic attractors in the system. Moreover, the Monte Carlo hypothesis test (or, equivalently, surrogate data test) is applied to the system for the detection of chaos.

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36

van Gelder, Tim. "Disentangling dynamics, computation, and cognition." Behavioral and Brain Sciences 21, no. 5 (October 1998): 654–61. http://dx.doi.org/10.1017/s0140525x98521735.

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The nature of the dynamical hypothesis in cognitive science (the DH) is further clarified in responding to various criticisms and objections raised in commentaries. Major topics addressed include the definitions of “dynamical system” and “digital computer”; the DH as Law of Qualitative Structure; the DH as an ontological claim; the multiple-realizability of dynamical models; the level at which the DH is formulated; the nature of dynamics; the role of representations in dynamical cognitive science; the falsifiability of the DH; the extent to which the DH is open; the role of temporal and implementation considerations; and the novelty or importance of the DH. The basic formulation and defense of the DH in the target article survives intact, though some refinements are recommended.

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Rossetto, Bruno, Thierry Lenzini, Sofiane Ramdani, and Gilles Suchey. "Slow-Fast Autonomous Dynamical Systems." International Journal of Bifurcation and Chaos 08, no. 11 (November 1998): 2135–45. http://dx.doi.org/10.1142/s0218127498001765.

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In this paper, we consider a class of slow-fast autonomous dynamical systems, i.e. systems having a small parameter ∊ multiplying a component of velocity. At first, the singular perturbation method (∊ = 0+) is recalled. Then we consider the case ∊ ≠ 0. Starting from a working hypothesis and particularly in the case of a singular approximation, our purpose is to show that there exists slow manifolds which can be defined as the slow manifolds of a so-called tangent linear system. The method allowed us to plot the slow manifold and to go further into the qualitative study and the geometric characterization of attractors. As an example, we give the explicit slow manifold equation of the van der Pol limit cycle. The value of the parameter corresponding to bifurcations is computed. Other third order systems are also treated. The method is extended to dynamical systems with no small parameter, and, therefore, which have no singular approximations, but have at least one real and negative eigenvalue in a large domain. It is numerically shown from the Lorenz model and from a laser model that there exists slow manifolds which can be defined as the slow manifods of a so-called tangent linear system, as in the previous cases. The implicit equation of these slow manifolds has been calculated too.

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38

Christos, George A. "Investigation of the Crick-Mitchison reverse-learning dream sleep hypothesis in a dynamical setting." Neural Networks 9, no. 3 (April 1996): 427–34. http://dx.doi.org/10.1016/0893-6080(95)00072-0.

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39

Khrennikov, Andrei. "Buonomano against Bell: Nonergodicity or nonlocality?" International Journal of Quantum Information 15, no. 08 (December 2017): 1740010. http://dx.doi.org/10.1142/s021974991740010x.

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The aim of this note is to attract attention of the quantum foundational community to the fact that in Bell’s arguments, one cannot distinguish two hypotheses: (a) quantum mechanics is nonlocal, (b) quantum mechanics is nonergodic. Therefore, experimental violations of Bell’s inequality can be as well interpreted as supporting the hypothesis that stochastic processes induced by quantum measurements are nonergodic. The latter hypothesis was discussed actively by Buonomano since 1980. However, in contrast to Bell’s hypothesis on nonlocality, it did not attract so much attention. The only experiment testing the hypothesis on nonergodicity was performed in neutron interferometry (by Summhammer, in 1989). This experiment can be considered as rejecting this hypothesis. However, it cannot be considered as a decisive experiment. New experiments are badly needed. We point out that a nonergodic model can be realistic, i.e. the distribution of hidden (local!) variables is well-defined. We also discuss coupling of violation of the Bell inequality with violation of the condition of weak mixing for ergodic dynamical systems.

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40

Paul, Prasenjit, Rikpratik Sengupta, and Saibal Ray. "Weyl transformation: A dynamical degree of freedom in the light of Dirac’s Large Number hypothesis." International Journal of Modern Physics D 29, no. 03 (February 2020): 2050027. http://dx.doi.org/10.1142/s0218271820500273.

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In Einstein’s Field Equation (EFE), the geometry of the spacetime is connected with the matter distribution. The geometry or the gravitational sector deals with classical macroscopic objects involving gravitational units while the matter sector can be better described by quantum theory involving atomic units. It has been argued by Bisabr [ arXiv:gr-qc/1904.09336 ] that there exists an epoch-dependent conversion factor between these two unit systems present in two different conformal frames, i.e. the conformal factor is epoch-dependent. We argue that the conformal transformation (CT) is a dynamical degree of freedom describing it’s possible relevance in inflation in context to the graceful exit problem, dynamics of the cosmological constant [Formula: see text] and justify the argument in the light of consequences of Dirac’s Large Number hypothesis (LNH).

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Cionco, Rodolfo G., and Rosa H. Compagnucci. "A new imminent grand minimum?" Proceedings of the International Astronomical Union 7, S286 (October 2011): 414–17. http://dx.doi.org/10.1017/s1743921312005169.

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AbstractThe planetary hypothesis of solar cycle is an old idea by which the planetary gravity acting on the Sun might have a non-negligible effect on the solar magnetic cycle. The advance of this hypothesis is based on phenomenological correlations between dynamical parameters of the Sun's movement around the barycenter of the Solar System and sunspots time series. In addition, several authors have proposed, using different methodologies that the first Grand Minima (GM) event of the new millennium is coming or has already begun. We present new fully three dimensional N-body simulations of the solar inertial motion (SIM) around the barycentre of the solar system in order to perform a phenomenological comparison between relevant SIM dynamical parameters and the occurrences of the last GM events (i.e., Maunder and Dalton). Our fundamental result is that the Sun acceleration decomposed in a co-orbital reference system shows a very particular behaviour that is common to Maunder minimum, Dalton minimum and the maximum of cycle 22 (around 1990), before the present prolonged minimum. We discuss our results in terms of a dynamical characterization of GM with relation to Sun dynamics and possible implications for a new GM event.

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Deco, Gustavo, and Edmund T. Rolls. "Neurodynamics of Biased Competition and Cooperation for Attention: A Model With Spiking Neurons." Journal of Neurophysiology 94, no. 1 (July 2005): 295–313. http://dx.doi.org/10.1152/jn.01095.2004.

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Recent neurophysiological experiments have led to a promising “ biased competition hypothesis” of the neural basis of attention. According to this hypothesis, attention appears as a sometimes nonlinear property that results from a top-down biasing effect that influences the competitive and cooperative interactions that work both within cortical areas and between cortical areas. In this paper we describe a detailed dynamical analysis of the synaptic and neuronal spiking mechanisms underlying biased competition. We perform a detailed analysis of the dynamical capabilities of the system by exploring the stationary attractors in the parameter space by a mean-field reduction consistent with the underlying synaptic and spiking dynamics. The nonstationary dynamical behavior, as measured in neuronal recording experiments, is studied by an integrate-and-fire model with realistic dynamics. This elucidates the role of cooperation and competition in the dynamics of biased competition and shows why feedback connections between cortical areas need optimally to be weaker by a factor of about 2.5 than the feedforward connections in an attentional network. We modeled the interaction between top-down attention and bottom-up stimulus contrast effects found neurophysiologically and showed that top-down attentional effects can be explained by external attention inputs biasing neurons to move to different parts of their nonlinear activation functions. Further, it is shown that, although NMDA nonlinear effects may be useful in attention, they are not necessary, with nonlinear effects (which may appear multiplicative) being produced in the way just described.

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GOLES, ERIC, and MARTÍN MATAMALA. "DYNAMICAL AND COMPLEXITY RESULTS FOR HIGH ORDER NEURAL NETWORKS." International Journal of Neural Systems 05, no. 03 (September 1994): 241–52. http://dx.doi.org/10.1142/s0129065794000256.

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We present dynamical results concerning neural networks with high order arguments. More precisely, we study the family of block-sequential iteration of neural networks with polynomial arguments. In this context, we prove that, under a symmetric hypothesis, the sequential iteration is the only one of this family to converge to fixed points. The other iteration modes present a highly complex dynamical behavior: non-bounded cycles and simulation of arbitrary non-symmetric linear neural network.5 We also study a high order memory iteration scheme which accepts an energy functional and bounded cycles in the size of the memory steps.

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Mattioni, L., J. P. Wittmer, J. Baschnagel, J. L. Barrat, and E. Luijten. "Dynamical properties of the slithering-snake algorithm: A numerical test of the activated-reptation hypothesis." European Physical Journal E 10, no. 4 (April 2003): 369–85. http://dx.doi.org/10.1140/epje/i2002-10122-1.

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Villalobos, Jorge, and Mauricio Vargas. "Towards a simple dynamical model of citizens’ perception." Kybernetes 44, no. 6/7 (June 1, 2015): 1134–45. http://dx.doi.org/10.1108/k-12-2014-0281.

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Purpose – The purpose of this paper is to propose a minimal dynamic two-dimensional map for the relation between citizens’ perception of quality of life (y) and their perception of the city Mayor management abilities (F). Design/methodology/approach – The authors use data from the Ciudades cómo vamos? project and test a simple hypothesis: there is a linear positive correlation between y and F. Following the authors propose a two-dimensional map based on ideas from a statistical regression model and a non-linear dynamical map on the [0; 1] interval. Findings – The authors give evidence that suggests that y and F are not linearly correlated. The authors show that the two-dimensional map, mentioned above, is able to reproduce non-trivial and unsynchronized relations between the variables, as well as the whole range of correlation coefficients. Research limitations/implications – There is a very limited amount of data to work with, therefore it was not possible to explore other possible relations thoroughly. Regarding the dynamical map, the authors are aware that there are still many venues for its study. Originality/value – To the authors’ knowledge, this is the first reported attempt at modeling the dynamics between two variables obtained via survey on which perception is a key component of the questions.

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Shi, Haibo, Yaoru Sun, and Jie Li. "Dynamical Motor Control Learned with Deep Deterministic Policy Gradient." Computational Intelligence and Neuroscience 2018 (2018): 1–11. http://dx.doi.org/10.1155/2018/8535429.

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Conventional models of motor control exploit the spatial representation of the controlled system to generate control commands. Typically, the control command is gained with the feedback state of a specific instant in time, which behaves like an optimal regulator or spatial filter to the feedback state. Yet, recent neuroscience studies found that the motor network may constitute an autonomous dynamical system and the temporal patterns of the control command can be contained in the dynamics of the motor network, that is, the dynamical system hypothesis (DSH). Inspired by these findings, here we propose a computational model that incorporates this neural mechanism, in which the control command could be unfolded from a dynamical controller whose initial state is specified with the task parameters. The model is trained in a trial-and-error manner in the framework of deep deterministic policy gradient (DDPG). The experimental results show that the dynamical controller successfully learns the control policy for arm reaching movements, while the analysis of the internal activities of the dynamical controller provides the computational evidence to the DSH of the neural coding in motor cortices.

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COOPERSTOCK, F. I. "DOES A DYNAMICAL SYSTEM LOSE ENERGY BY EMITTING GRAVITATIONAL WAVES?" Modern Physics Letters A 14, no. 23 (July 30, 1999): 1531–37. http://dx.doi.org/10.1142/s0217732399001620.

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We note that Eddington's radiation damping calculation of a spinning rod fails to account for the complete mass integral as given by Tolman. The missing stress contributions precisely cancel the standard rate given by the "quadrupole formula". This indicates that while the usual "kinetic" term can properly account for dynamical changes in the source, the actual mass is conserved. Hence gravity waves are not carriers of energy in vacuum. This supports the hypothesis that energy including the gravitational contribution is confined to regions of nonvanishing energy–momentum tensor Tik.

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Chung, Jin-Seok, and Stephen M. Durbin. "Temperature-dependent X-ray dynamical diffraction: Darwin theory simulations." Acta Crystallographica Section A Foundations of Crystallography 55, no. 1 (January 1, 1999): 14–19. http://dx.doi.org/10.1107/s0108767398006898.

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Thermal vibrations destroy the perfect crystalline periodicity generally assumed by dynamical diffraction theories. This can lead to some difficulty in deriving the temperature dependence of X-ray reflectivity from otherwise perfect crystals. This difficulty is overcome here in numerical simulations based on the extended Darwin theory, which does not require periodicity. Using Si and Ge as model materials, it is shown how to map the lattice vibrations derived from measured phonon dispersion curves onto a suitable Darwin model. Good agreement is observed with the usual Debye–Waller behavior predicted by standard theories, except at high temperatures for high-order reflections. These deviations are discussed in terms of a possible breakdown of the ergodic hypothesis for X-ray diffraction.

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Napier, W. M. "Dynamical interactions of the solar system with massive nebulae." International Astronomical Union Colloquium 83 (1985): 31–41. http://dx.doi.org/10.1017/s0252921100083780.

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AbstractThe effects of encounters with massive nebulae on the long-period comet population are examined, paying particular attention to the uncertainties in the data. An earlier conclusion, that the long-period comet system is dynamically unstable, is upheld. Whether replenishment by unbinding from a dense inner comet cloud is a viable hypothesis awaits detailed modelling, but a qualitative discussion is given which argues tentatively against it. If comets occur in molecular clouds, however, their capture into temporarily bound Solar System orbits is a natural consequence of close encounters for realistic velocities and potentials. A large disturbance or capture may have occurred a few Myr ago as the Sun emerged from the Orion spiral arm.

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Gogilashvili, Mariam, Jeremiah W. Murphy, and Quintin Mabanta. "Explosion energies for core-collapse supernovae I: analytic, spherically symmetric solutions." Monthly Notices of the Royal Astronomical Society 500, no. 4 (November 13, 2020): 5393–407. http://dx.doi.org/10.1093/mnras/staa3546.

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ABSTRACT Recent multidimensional simulations of core-collapse supernovae are producing successful explosions and explosion-energy predictions. In general, the explosion-energy evolution is monotonic and relatively smooth, suggesting a possible analytic solution. We derive analytic solutions for the expansion of the gain region under the following assumptions: spherical symmetry, one-zone shell, and powered by neutrinos and α particle recombination. We consider two hypotheses: (I) explosion energy is powered by neutrinos and α recombination and (II) explosion energy is powered by neutrinos alone. Under these assumptions, we derive the fundamental dimensionless parameters and analytic scalings. For the neutrino-only hypothesis (II), the asymptotic explosion energy scales as $E_{\infty } \approx 1.5 M_\mathrm{ g}\nu _0^2 \eta ^{2/3}$, where Mg is the gain mass, $\nu _0$ is the free-fall velocity at the shock, and η is a ratio of the heating and dynamical time-scales. Including both neutrinos and recombination (hypothesis I), the asymptotic explosion energy is $E_{\infty } \approx M_g \nu _0^2 (1.5\eta ^{2/3} + \beta f(\rho _0))$, where β is the dimensionless recombination parameter. We use Bayesian inference to fit these analytic models to simulations. Both hypotheses fit the simulations of the lowest progenitor masses that tend to explode spherically. The fits do not prefer hypothesis I or II; however, prior investigations suggest that α recombination is important. As expected, neither hypothesis fits the higher mass simulations that exhibit aspherical explosions. In summary, this explosion energy theory is consistent with the spherical explosions of low progenitor masses; the inconsistency with higher progenitor-mass simulations suggests that a theory for them must include aspherical dynamics.

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