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Journal articles on the topic 'Lévy systems'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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1

Klafter, J., G. Zumofen, and M. F. Shlesinger. "Lévy walks in dynamical systems." Physica A: Statistical Mechanics and its Applications 200, no. 1-4 (1993): 222–30. http://dx.doi.org/10.1016/0378-4371(93)90520-e.

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2

Volpert, V. A., Y. Nec, and A. A. Nepomnyashchy. "Fronts in anomalous diffusion–reaction systems." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1982 (2013): 20120179. http://dx.doi.org/10.1098/rsta.2012.0179.

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A review of recent developments in the field of front dynamics in anomalous diffusion–reaction systems is presented. Both fronts between stable phases and those propagating into an unstable phase are considered. A number of models of anomalous diffusion with reaction are discussed, including models with Lévy flights, truncated Lévy flights, subdiffusion-limited reactions and models with intertwined subdiffusion and reaction operators.

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3

Drysdale, P. M., and P. A. Robinson. "Lévy random walks in finite systems." Physical Review E 58, no. 5 (1998): 5382–94. http://dx.doi.org/10.1103/physreve.58.5382.

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4

Manwadkar, Viraj, Alessandro A. Trani, and Nathan W. C. Leigh. "Chaos and Lévy flights in the three-body problem." Monthly Notices of the Royal Astronomical Society 497, no. 3 (2020): 3694–712. http://dx.doi.org/10.1093/mnras/staa1722.

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ABSTRACT We study chaos and Lévy flights in the general gravitational three-body problem. We introduce new metrics to characterize the time evolution and final lifetime distributions, namely Scramble Density $\mathcal {S}$ and the Lévy flight (LF) index $\mathcal {L}$, that are derived from the Agekyan–Anosova maps and homology radius $R_{\mathcal {H}}$. Based on these metrics, we develop detailed procedures to isolate the ergodic interactions and Lévy flight interactions. This enables us to study the three-body lifetime distribution in more detail by decomposing it into the individual distrib

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5

Liu, Meng, and Ke Wang. "Stochastic Lotka–Volterra systems with Lévy noise." Journal of Mathematical Analysis and Applications 410, no. 2 (2014): 750–63. http://dx.doi.org/10.1016/j.jmaa.2013.07.078.

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6

Qiao, Huijie, and Jinqiao Duan. "Nonlinear filtering of stochastic dynamical systems with Lévy noises." Advances in Applied Probability 47, no. 03 (2015): 902–18. http://dx.doi.org/10.1017/s0001867800048886.

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Nonlinear filtering is investigated in a system where both the signal system and the observation system are under non-Gaussian Lévy fluctuations. Firstly, the Zakai equation is derived, and it is further used to derive the Kushner-Stratonovich equation. Secondly, by a filtered martingale problem, uniqueness for strong solutions of the Kushner-Stratonovich equation and the Zakai equation is proved. Thirdly, under some extra regularity conditions, the Zakai equation for the unnormalized density is also derived in the case of α-stable Lévy noise.

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7

Qiao, Huijie, and Jinqiao Duan. "Nonlinear filtering of stochastic dynamical systems with Lévy noises." Advances in Applied Probability 47, no. 3 (2015): 902–18. http://dx.doi.org/10.1239/aap/1444308887.

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Nonlinear filtering is investigated in a system where both the signal system and the observation system are under non-Gaussian Lévy fluctuations. Firstly, the Zakai equation is derived, and it is further used to derive the Kushner-Stratonovich equation. Secondly, by a filtered martingale problem, uniqueness for strong solutions of the Kushner-Stratonovich equation and the Zakai equation is proved. Thirdly, under some extra regularity conditions, the Zakai equation for the unnormalized density is also derived in the case of α-stable Lévy noise.

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8

QIAO, HUIJIE, and JINQIAO DUAN. "TOPOLOGICAL EQUIVALENCE FOR DISCONTINUOUS RANDOM DYNAMICAL SYSTEMS AND APPLICATIONS." Stochastics and Dynamics 14, no. 01 (2013): 1350007. http://dx.doi.org/10.1142/s021949371350007x.

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After defining non-Gaussian Lévy processes for two-sided time, stochastic differential equations with such Lévy processes are considered. Solution paths for these stochastic differential equations have countable jump discontinuities in time. Topological equivalence (or conjugacy) for such an Itô stochastic differential equation and its transformed random differential equation is established. Consequently, a stochastic Hartman–Grobman theorem is proved for the linearization of the Itô stochastic differential equation. Furthermore, for Marcus stochastic differential equations, this topological e

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9

Sibatov, Renat T., and HongGuang Sun. "Tempered Fractional Equations for Quantum Transport in Mesoscopic One-Dimensional Systems with Fractal Disorder." Fractal and Fractional 3, no. 4 (2019): 47. http://dx.doi.org/10.3390/fractalfract3040047.

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New aspects of electron transport in quantum wires with Lévy-type disorder are described. We study the weak scattering and the incoherent sequential tunneling in one-dimensional quantum systems characterized by a tempered Lévy stable distribution of spacing between scatterers or tunneling barriers. The generalized Dorokhov–Mello–Pereyra–Kumar equation contains the tempered fractional derivative on wire length. The solution describes the evolution from the anomalous conductance distribution to the Dorokhov function for a long wire. For sequential tunneling, average values and relative fluctuati

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10

Fricke, G. M., J. P. Hecker, J. L. Cannon, and M. E. Moses. "Immune-inspired search strategies for robot swarms." Robotica 34, no. 8 (2016): 1791–810. http://dx.doi.org/10.1017/s0263574716000382.

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SUMMARYDetection of targets distributed randomly in space is a task common to both robotic and biological systems. Lévy search has previously been used to characterize T cell search in the immune system. We use a robot swarm to evaluate the effectiveness of a Lévy search strategy and map the relationship between search parameters and target configurations. We show that the fractal dimension of the Lévy search which optimizes search efficiency depends strongly on the distribution of targets but only weakly on the number of agents involved in search. Lévy search can therefore be tuned to the tar

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11

Volkov, Boris O. "Lévy differential operators and Gauge invariant equations for Dirac and Higgs fields." Infinite Dimensional Analysis, Quantum Probability and Related Topics 22, no. 01 (2019): 1950001. http://dx.doi.org/10.1142/s0219025719500012.

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We study the Lévy infinite-dimensional differential operators (differential operators defined by the analogy with the Lévy Laplacian) and their relationship to the Yang–Mills equations. We consider the parallel transport on the space of curves as an infinite-dimensional analogue of chiral fields and show that it is a solution to the system of differential equations if and only if the associated connection is a solution to the Yang–Mills equations. This system is an analogue of the equations of motion of chiral fields and contains the Lévy divergence. The systems of infinite-dimensional equatio

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12

Denisov, S., J. Klafter, M. Urbakh, and S. Flach. "DC currents in Hamiltonian systems by Lévy flights." Physica D: Nonlinear Phenomena 170, no. 2 (2002): 131–42. http://dx.doi.org/10.1016/s0167-2789(02)00545-6.

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13

Zumofen, G., J. Klafter, and A. Blumen. "Lévy walks and propagators in intermittent chaotic systems." Physical Review E 47, no. 3 (1993): 2183–86. http://dx.doi.org/10.1103/physreve.47.2183.

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14

Shkolnikov, Mykhaylo. "Competing particle systems evolving by interacting Lévy processes." Annals of Applied Probability 21, no. 5 (2011): 1911–32. http://dx.doi.org/10.1214/10-aap743.

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15

APPLEBAUM, DAVID, and MICHAILINA SIAKALLI. "STOCHASTIC STABILIZATION OF DYNAMICAL SYSTEMS USING LÉVY NOISE." Stochastics and Dynamics 10, no. 04 (2010): 509–27. http://dx.doi.org/10.1142/s0219493710003066.

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We investigate the perturbation of the nonlinear differential equation [Formula: see text] by random noise terms consisting of Brownian motion and an independent Poisson random measure. We find conditions under which the perturbed system is almost surely exponentially stable and estimate the corresponding Lyapunov exponents.

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16

Abe, Masato S. "Functional advantages of Lévy walks emerging near a critical point." Proceedings of the National Academy of Sciences 117, no. 39 (2020): 24336–44. http://dx.doi.org/10.1073/pnas.2001548117.

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A special class of random walks, so-called Lévy walks, has been observed in a variety of organisms ranging from cells, insects, fishes, and birds to mammals, including humans. Although their prevalence is considered to be a consequence of natural selection for higher search efficiency, some findings suggest that Lévy walks might also be epiphenomena that arise from interactions with the environment. Therefore, why they are common in biological movements remains an open question. Based on some evidence that Lévy walks are spontaneously generated in the brain and the fact that power-law distribu

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17

Högele, Michael, and Ilya Pavlyukevich. "Metastability in a class of hyperbolic dynamical systems perturbed by heavy-tailed Lévy type noise." Stochastics and Dynamics 15, no. 03 (2015): 1550019. http://dx.doi.org/10.1142/s0219493715500197.

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We consider a finite dimensional deterministic dynamical system with finitely many local attractors Kι, each of which supports a unique ergodic probability measure Pι, perturbed by a multiplicative non-Gaussian heavy-tailed Lévy noise of small intensity ε > 0. We show that the random system exhibits a metastable behavior: there exists a unique ε-dependent time scale on which the system reminds of a continuous time Markov chain on the set of the invariant measures Pι. In particular our approach covers the case of dynamical systems of Morse–Smale type, whose attractors consist of points and l

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18

TYRAN-KAMIŃSKA, MARTA. "WEAK CONVERGENCE TO LÉVY STABLE PROCESSES IN DYNAMICAL SYSTEMS." Stochastics and Dynamics 10, no. 02 (2010): 263–89. http://dx.doi.org/10.1142/s0219493710002942.

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We study convergence of normalized ergodic sum processes to Lévy stable process in the Skorohod space with J1-topology. Our necessary and sufficient conditions allow us to prove or disprove such convergence for specific examples.

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19

Ortobelli Lozza, Sergio, Enrico Angelelli, and Alda Ndoci. "Timing portfolio strategies with exponential Lévy processes." Computational Management Science 16, no. 1-2 (2018): 97–127. http://dx.doi.org/10.1007/s10287-018-0332-y.

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20

Kuhwald, Isabelle, and Ilya Pavlyukevich. "Stochastic resonance with multiplicative heavy-tailed Lévy noise: Optimal tuning on an algebraic time scale." Stochastics and Dynamics 17, no. 04 (2017): 1750027. http://dx.doi.org/10.1142/s0219493717500277.

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Stochastic resonance is an amplification and synchronization effect of weak periodic signals in nonlinear systems through a small noise perturbation. In this paper we study the dynamics of stochastic resonance in a bistable system driven by multiplicative Lévy noise with heavy tails, e.g., [Formula: see text]-stable Lévy noise. We determine the optimal tuning with respect to a probabilistic synchronization measure for both the jump-diffusion and the reduced two-state Markov chain. These results extend the theory of stochastic resonance to the case of heavy tail Lévy perturbations.

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21

Santos, Maike A. F. dos. "Mittag–Leffler Memory Kernel in Lévy Flights." Mathematics 7, no. 9 (2019): 766. http://dx.doi.org/10.3390/math7090766.

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In this article, we make a detailed study of some mathematical aspects associated with a generalized Lévy process using fractional diffusion equation with Mittag–Leffler kernel in the context of Atangana–Baleanu operator. The Lévy process has several applications in science, with a particular emphasis on statistical physics and biological systems. Using the continuous time random walk, we constructed a fractional diffusion equation that includes two fractional operators, the Riesz operator to Laplacian term and the Atangana–Baleanu in time derivative, i.e., a A B D t α ρ ( x , t ) = K α , μ ∂

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22

Grigoriu, M. "Equivalent linearization for systems driven by Lévy white noise." Probabilistic Engineering Mechanics 15, no. 2 (2000): 185–90. http://dx.doi.org/10.1016/s0266-8920(99)00018-1.

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23

Engelke, Sebastian, and Zakhar Kabluchko. "Max-stable processes and stationary systems of Lévy particles." Stochastic Processes and their Applications 125, no. 11 (2015): 4272–99. http://dx.doi.org/10.1016/j.spa.2015.07.001.

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24

Zhou, Ji-Lin, and Yi-Sui Sun. "Lévy flights in comet motion and related chaotic systems." Physics Letters A 287, no. 3-4 (2001): 217–22. http://dx.doi.org/10.1016/s0375-9601(01)00482-0.

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25

Boxma, Onno, Jevgenijs Ivanovs, Kamil Kosiński, and Michel Mandjes. "Lévy-driven Polling Systems and Continuous-State Branching Processes." Stochastic Systems 1, no. 2 (2011): 411–36. http://dx.doi.org/10.1287/10-ssy008.

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26

Redmann, Martin, and Peter Benner. "Singular perturbation approximation for linear systems with Lévy noise." Stochastics and Dynamics 18, no. 04 (2018): 1850033. http://dx.doi.org/10.1142/s0219493718500338.

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To solve a stochastic linear evolution equation numerically, finite dimensional approximations are commonly used. For a good approximation, one might end up with a sequence of ordinary stochastic linear equations of high order. To reduce the high dimension for practical computations, we consider the singular perturbation approximation as a model order reduction technique in this paper. This approach is well-known from deterministic control theory and here we generalize it for controlled linear systems with Lévy noise. Additionally, we discuss properties of the reduced order model, provide an e

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27

He, Danhua. "Boundedness theorems of stochastic differential systems with Lévy noise." Applied Mathematics Letters 106 (August 2020): 106358. http://dx.doi.org/10.1016/j.aml.2020.106358.

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28

Xu, Yong, Xi-Ying Wang, Hui-Qing Zhang, and Wei Xu. "Stochastic stability for nonlinear systems driven by Lévy noise." Nonlinear Dynamics 68, no. 1-2 (2011): 7–15. http://dx.doi.org/10.1007/s11071-011-0199-8.

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29

He, Hui, Zenghu Li, and Xiaowen Zhou. "Branching particle systems in spectrally one-sided Lévy processes." Frontiers of Mathematics in China 10, no. 4 (2015): 875–900. http://dx.doi.org/10.1007/s11464-015-0473-z.

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30

Fralix, Brian H., Johan S. H. van Leeuwaarden, and Onno J. Boxma. "Factorization Identities for Reflected Processes, with Applications." Journal of Applied Probability 50, no. 03 (2013): 632–53. http://dx.doi.org/10.1017/s002190020000975x.

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We derive factorization identities for a class of preemptive-resume queueing systems, with batch arrivals and catastrophes that, whenever they occur, eliminate multiple customers present in the system. These processes are quite general, as they can be used to approximate Lévy processes, diffusion processes, and certain types of growth‒collapse processes; thus, all of the processes mentioned above also satisfy similar factorization identities. In the Lévy case, our identities simplify to both the well-known Wiener‒Hopf factorization, and another interesting factorization of reflected Lévy proce

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31

Fralix, Brian H., Johan S. H. van Leeuwaarden, and Onno J. Boxma. "Factorization Identities for Reflected Processes, with Applications." Journal of Applied Probability 50, no. 3 (2013): 632–53. http://dx.doi.org/10.1239/jap/1378401227.

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We derive factorization identities for a class of preemptive-resume queueing systems, with batch arrivals and catastrophes that, whenever they occur, eliminate multiple customers present in the system. These processes are quite general, as they can be used to approximate Lévy processes, diffusion processes, and certain types of growth‒collapse processes; thus, all of the processes mentioned above also satisfy similar factorization identities. In the Lévy case, our identities simplify to both the well-known Wiener‒Hopf factorization, and another interesting factorization of reflected Lévy proce

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32

Sheykin, Anton, and Sergey Manida. "Universal Constants and Natural Systems of Units in a Spacetime of Arbitrary Dimension." Universe 6, no. 10 (2020): 166. http://dx.doi.org/10.3390/universe6100166.

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We study the properties of fundamental physical constants using the threefold classification of dimensional constants proposed by J.-M. Lévy-Leblond: constants of objects (masses, etc.), constants of phenomena (coupling constants), and “universal constants” (such as c and ℏ). We show that all of the known “natural” systems of units contain at least one non-universal constant. We discuss the possible consequences of such non-universality, e.g., the dependence of some of these systems on the number of spatial dimensions. In the search for a “fully universal” system of units, we propose a set of

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33

Gu, Anhui, Yangrong Li та Jia Li. "Random Attractors on Lattice of Stochastic FitzHugh–Nagumo Systems Driven by α-Stable Lévy Noises". International Journal of Bifurcation and Chaos 24, № 10 (2014): 1450123. http://dx.doi.org/10.1142/s0218127414501235.

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34

KLAFTER, J., G. ZUMOFEN, and M. F. SHLESINGER. "FRACTAL DESCRIPTION OF ANOMALOUS DIFFUSION IN DYNAMICAL SYSTEMS." Fractals 01, no. 03 (1993): 389–404. http://dx.doi.org/10.1142/s0218348x93000411.

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Anomalous diffusion properties are common in a broad spectrum of systems including dynamical systems. In this paper we review an approach based on Lévy scale-invariant distributions to describe transport in dynamical systems. We introduce the basic ingredients that make the approach useful in describing anomalous diffusion and demonstrate the applicability in the cases of one-dimensional iterated maps and of the standard map.

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35

Rodriguez-Aguilar, Roman. "A Hybrid Model to Simulate Test Cases of Electrical Power Systems." Applied Sciences 10, no. 10 (2020): 3531. http://dx.doi.org/10.3390/app10103531.

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The development of solution algorithms for power system problems is based on hypothetical test systems and test cases. These systems are very scarce, and the degree of variability is relatively low. The constant development of the economic analysis in electrical power systems denotes the need to obtain standardized systems and cases. In this study, the creation of standardized test cases based on a hybrid model using Lévy alpha stable distributions and generalized additive models is proposed. The objective of the work is to present a methodological proposal for the creation of test environment

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36

CABRERA, JUAN LUIS, RONALD BORMANN, CHRISTIAN EURICH, TORU OHIRA, and JOHN MILTON. "STATE-DEPENDENT NOISE AND HUMAN BALANCE CONTROL." Fluctuation and Noise Letters 04, no. 01 (2004): L107—L117. http://dx.doi.org/10.1142/s0219477504001719.

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The fluctuations observed in the task of stick balancing at the fingertip exhibit many of the properties predicted to occur in parametric stochastic dynamical systems, namely intermittency, truncated Lévy flights and truncated Lévy distributions. The development of virtual balancing tasks that involve the interplay between a human and computer and that exhibit the same dynamical properties as seen for stick balancing opens the door for experimental investigations into the nature of the neural motor control mechanisms that underlie these phenomena.

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37

Xu, Yong, Jinqiao Duan, and Wei Xu. "An averaging principle for stochastic dynamical systems with Lévy noise." Physica D: Nonlinear Phenomena 240, no. 17 (2011): 1395–401. http://dx.doi.org/10.1016/j.physd.2011.06.001.

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38

Gupta, Hari M., and José R. Campanha. "The gradually truncated Lévy flight: stochastic process for complex systems." Physica A: Statistical Mechanics and its Applications 275, no. 3-4 (2000): 531–43. http://dx.doi.org/10.1016/s0378-4371(99)00367-2.

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39

Gu, Anhui. "Synchronization of Coupled Stochastic Systems Driven byα-Stable Lévy Noises". Mathematical Problems in Engineering 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/685798.

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The synchronization of the solutions to coupled stochastic systems ofN-Marcus stochastic ordinary differential equations which are driven byα-stable Lévy noises is investigated(N∈ℕ,1<α<2). We obtain the synchronization between two solutions and among different components of solutions under certain dissipative conditions. The synchronous phenomena persist no matter how large the intensity of the environment noises. These results generalize the work of two Marcus canonical equations in X. M. Liu et al.' s (2010).

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40

Dybiec, Bartłomiej, and Ewa Gudowska-Nowak. "Bimodality and hysteresis in systems driven by confined Lévy flights." New Journal of Physics 9, no. 12 (2007): 452. http://dx.doi.org/10.1088/1367-2630/9/12/452.

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41

Kuhwald, Isabelle, та Ilya Pavlyukevich. "Stochastic Resonance in Systems Driven by α-Stable Lévy Noise". Procedia Engineering 144 (2016): 1307–14. http://dx.doi.org/10.1016/j.proeng.2016.05.129.

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42

Zhou, Hui, Yueying Li, and Wenxue Li. "Synchronization for stochastic hybrid coupled controlled systems with Lévy noise." Mathematical Methods in the Applied Sciences 43, no. 17 (2020): 9557–81. http://dx.doi.org/10.1002/mma.6624.

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43

He, Danhua, and Liguang Xu. "Boundedness analysis of stochastic integro-differential systems with Lévy noise." Journal of Taibah University for Science 14, no. 1 (2019): 87–93. http://dx.doi.org/10.1080/16583655.2019.1708540.

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44

Nec, Y., A. A. Nepomnyashchy, and A. A. Golovin. "Weakly nonlinear dynamics in reaction–diffusion systems with Lévy flights." Physica Scripta T132 (December 2008): 014043. http://dx.doi.org/10.1088/0031-8949/2008/t132/014043.

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45

Do, K. D. "Inverse optimal control of stochastic systems driven by Lévy processes." Automatica 107 (September 2019): 539–50. http://dx.doi.org/10.1016/j.automatica.2019.06.016.

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46

Lü, Yan, and Hong Lu. "Anomalous Dynamics of Inertial Systems Driven by Colored Lévy Noise." Journal of Statistical Physics 176, no. 4 (2019): 1046–56. http://dx.doi.org/10.1007/s10955-019-02331-2.

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47

Chao, Ying, Pingyuan Wei, and Jinqiao Duan. "Lyapunov exponents for Hamiltonian systems under small Lévy-type perturbations." Chaos: An Interdisciplinary Journal of Nonlinear Science 31, no. 8 (2021): 081101. http://dx.doi.org/10.1063/5.0058716.

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48

Żaba, Mariusz, and Piotr Garbaczewski. "Thermalization of Lévy Flights: Path-Wise Picture in 2D." International Journal of Statistical Mechanics 2013 (October 3, 2013): 1–11. http://dx.doi.org/10.1155/2013/738345.

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We analyze two-dimensional (2D) random systems driven by a symmetric Lévy stable noise which in the presence of confining potentials may asymptotically set down at Boltzmann-type thermal equilibria. In view of the Eliazar-Klafter no-go statement, such dynamical behavior is plainly incompatible with the standard Langevin modeling of Lévy flights. No explicit path-wise description has been so far devised for the thermally equilibrating random motion we address, and its formulation is the principal goal of the present work. To this end we prescribe a priori the target pdf ρ∗ in the Boltzmann form

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49

Santhosh, Kumar G., Sumesh Gopinath, and P. R. Prince. "A study on universality, non-extensivity and Lévy statistics of solar wind turbulence." Proceedings of the International Astronomical Union 13, S340 (2018): 65–66. http://dx.doi.org/10.1017/s1743921318001618.

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AbstractA number of complex systems arising in diverse disciplines may have certain quantitative features that are surprisingly similar which are classified under the paradigm of “universality”. The non-extensive Tsallis stastical mechanics and Lévy flight patterns provide a novel basis for analyzing non-equilibrium complex systems that may exhibit long-range correlations. The present work studies the scope of employing non-extensive Gutenberg-Richter (G-R) type law for the magnitude distribution of energy of solar wind, in order to investigate the existence of a universal behavior as well as

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50

Singla, Rohit, Harish Parthasarathy, and Vijyant Agarwal. "Classical robots perturbed by Lévy processes: analysis and Lévy disturbance rejection methods." Nonlinear Dynamics 89, no. 1 (2017): 553–75. http://dx.doi.org/10.1007/s11071-017-3471-8.

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