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Journal articles on the topic 'Dissipativeness'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 July 2025

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1

WEILAND, SIEP, and JAN C. WILLEMS. "DISSIPATIVE DYNAMICAL SYSTEMS IN A BEHAVIORAL CONTEXT." Mathematical Models and Methods in Applied Sciences 01, no. 01 (1991): 1–25. http://dx.doi.org/10.1142/s0218202591000022.

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Various conceptual definitions of dissipativeness of time invariant dynamical systems are introduced. A formal distinction is made between external and internal dissipativeness and it is shown that, under certain conditions, these notions are equivalent. A characterization of the class of internal storage functions associated with a dissipative system is given. The results are applied to the class of finite-dimensional linear time invariant systems. Necessary and sufficient conditions for dissipativeness of systems in this class are derived and the relation to LQ-theory is discussed.

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2

Gurney, David R. "Generalized dissipativeness in a Banach space." International Journal of Mathematics and Mathematical Sciences 19, no. 1 (1996): 25–32. http://dx.doi.org/10.1155/s0161171296000051.

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SupposeXis a real or complex Banach space with dualX*and a semiscalar product[,]. Forka real number, a subsetBofX×Xwill be calledk-dissipativeif for each pair of elements(x1,y1),(x2,y2)inB, there existsh∈{f∈X*:[x,f]=|x|2=|f|2}such thatRe[y1−y2,h]≤k|x1−x2|2.This definition extends a notion of dissipativeness which is equivalent to havingkequal zero here. A number of definitions and theorems related to this original dissipative notion are generalized in the present paper to fit thek-dissipative situation, and proofs are given for the new theorems.

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3

Kaneko, Osamu, and Takao Fujii. "DISCRETE TIME DISSIPATIVENESS ON THE DIPOLYNOMIAL RING." IFAC Proceedings Volumes 35, no. 1 (2002): 237–42. http://dx.doi.org/10.3182/20020721-6-es-1901.00201.

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4

Yong, Wen-An. "Intrinsic properties of conservation-dissipation formalism of irreversible thermodynamics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2170 (2020): 20190177. http://dx.doi.org/10.1098/rsta.2019.0177.

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This paper proposes four fundamental requirements for establishing PDEs (partial differential equations) modelling irreversible processes. We show that the PDEs derived via the CDF (conservation-dissipation formalism) meet all the requirements. In doing so, we find useful constraints on the freedoms of CDF and point out that a shortcoming of the formalism can be remedied with the help of the Maxwell iteration. It is proved that the iteration preserves the gradient structure and strong dissipativeness of the CDF-based PDEs. A refined formulation of the second law of thermodynamics is given to c

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5

SAVKIN, ANDREY V., and IAN R. PETERSEN. "Structured dissipativeness and absolute stability of nonlinear systems." International Journal of Control 62, no. 2 (1995): 443–60. http://dx.doi.org/10.1080/00207179508921550.

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6

HODAKA, Ichijyo, Masayuki SUZUKI, and Noboru SAKAMOTO. "Robust Control Based on Dissipativeness of Open-Loop Systems." Transactions of the Institute of Systems, Control and Information Engineers 12, no. 9 (1999): 549–57. http://dx.doi.org/10.5687/iscie.12.549.

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7

Chiu, Chuang-Hsiung, Wen-Wei Lin, and Chern-Shuh Wang. "Synchronization in a Lattice of Coupled van der Pol Systems." International Journal of Bifurcation and Chaos 08, no. 12 (1998): 2353–73. http://dx.doi.org/10.1142/s0218127498001893.

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We consider a lattice of coupled van der Pol systems with external periodic forces and Dirichlet boundary conditions. Under the assumption of bounded dissipativeness, we prove that the asymptotic synchronization occurs provided that the coupling coefficients are sufficiently large. Furthermore, we demonstrate from numerical simulations that asymptotic synchronization is affected by the coupling coefficients and the size of lattice.

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8

Bhat, M. S., and S. K. Shrivastava. "Dissipativeness and Stability of a Class of Distributed Parameter Systems." Journal of Applied Mechanics 52, no. 2 (1985): 471–76. http://dx.doi.org/10.1115/1.3169071.

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Input-output stability of linear-distributed parameter systems of arbitrary order and type in the presence of a distributed controller is analyzed by extending the concept of dissipativeness, with certain modifications, to such systems. The approach is applicable to systems with homogeneous or homogenizable boundary conditions. It also helps in generating a Liapunov functional to assess asymptotic stability of the system.

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9

RODRÍGUEZ-BERNAL, ANÍBAL. "SOME QUALITATIVE DYNAMICS OF NONLINEAR BOUNDARY CONDITIONS." International Journal of Bifurcation and Chaos 12, no. 11 (2002): 2333–42. http://dx.doi.org/10.1142/s0218127402005893.

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In this paper we survey some recent results on the behavior of solutions of parabolic equations subjected to nonlinear boundary conditions. The results range from local existence and regularity of solutions, to global existence, dissipativeness and existence of attractors, and to blow-up in finite time. Some applications are given to some singular perturbation problems and to pattern formation from boundary flux.

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10

Jiang, Xin. "Global Dynamics for an Age-Structured Cholera Infection Model with General Infection Rates." Mathematics 9, no. 23 (2021): 2993. http://dx.doi.org/10.3390/math9232993.

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This paper studies the global dynamics of a cholera model incorporating age structures and general infection rates. First, we explore the existence and point dissipativeness of the orbit and analyze the asymptotical smoothness. Then, we perform rigorous mathematical analysis on the existence and local stability of equilibria. Based on the uniform persistence, we further investigate the global behavior of the cholera infection model. The results of theoretical analysis are well confirmed by numerical simulations. This research generalizes some known results and provides deeper insights into the

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11

Jiang, Xin, and Ran Zhang. "Global dynamics on a class of age-infection structured cholera model with immigration." Electronic Journal of Qualitative Theory of Differential Equations, no. 6 (2023): 1–26. http://dx.doi.org/10.14232/ejqtde.2023.1.6.

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This paper is concerned with a class of age-structured cholera model with general infection rates. We first explore the existence and uniqueness, dissipativeness and persistence of the solutions, and the existence of the global attractor by verifying the asymptotical smoothness of the orbits. We then give mathematical analysis on the existence and local stability of the positive equilibrium. Based on the preparation, we further investigate the global behavior of the cholera infection model. Corresponding numerical simulations have been presented. Our results improve and generalize some known r

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12

CHRISTOFOROU, CLEOPATRA. "SYSTEMS OF HYPERBOLIC CONSERVATION LAWS WITH MEMORY." Journal of Hyperbolic Differential Equations 04, no. 03 (2007): 435–78. http://dx.doi.org/10.1142/s0219891607001215.

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Global weak solutions of bounded variation to systems of balance laws with non-local source are constructed by the method of vanishing viscosity. Suitable dissipativeness assumptions are imposed on the source terms to assure convergence of the method. Under these hypotheses, the total variation remains uniformly bounded and integrable in time, the vanishing viscosity solutions are uniformly stable in L1with respect to the initial data and converge to equilibrium as t → ∞. The motivation to study these systems is the observation that conservations laws with fading memory can be written in such

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13

Pakshin, P. V. "Exponential dissipativeness of the random-structure diffusion processes and problems of robust stabilization." Automation and Remote Control 68, no. 10 (2007): 1852–70. http://dx.doi.org/10.1134/s0005117907100128.

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14

Li, Chun-Hsien, and Suh-Yuh Yang. "Eventual dissipativeness and synchronization of nonlinearly coupled dynamical network of Hindmarsh–Rose neurons." Applied Mathematical Modelling 39, no. 21 (2015): 6631–44. http://dx.doi.org/10.1016/j.apm.2015.02.017.

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15

RODRIGUES, HILDEBRANDO M., JIANHONG WU, and LUÍS R. A. GABRIEL. "UNIFORM DISSIPATIVENESS, ROBUST SYNCHRONIZATION AND LOCATION OF THE ATTRACTOR OF PARAMETRIZED NONAUTONOMOUS DISCRETE SYSTEMS." International Journal of Bifurcation and Chaos 21, no. 02 (2011): 513–26. http://dx.doi.org/10.1142/s0218127411028568.

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In this series of papers, we study issues related to the synchronization of two coupled chaotic discrete systems arising from secured communication. The first part deals with uniform dissipativeness with respect to parameter variation via the Liapunov direct method. We obtain uniform estimates of the global attractor for a general discrete nonautonomous system, that yields a uniform invariance principle in the autonomous case. The Liapunov function is allowed to have positive derivative along solutions of the system inside a bounded set, and this reduces substantially the difficulty of constru

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16

Giles, P. T., and S. B. McCann. "Foredune development on Îles de la Madeleine (Quebec), Atlantic Canada." Canadian Journal of Earth Sciences 34, no. 11 (1997): 1467–76. http://dx.doi.org/10.1139/e17-119.

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The foredune, in this cool-temperate, sediment-abundant, relatively high wind and wave energy environment, is generally a single ridge with a mean height of 5.1 m (max. 11.4 m) and width of 25–35 m. Pioneer vegetation is dominated by Ammophila breviligulata. Four foredune types were identified: scarped, scarped with blowouts, scarped with incipient foredune, and nonscarped, the first being the most common, occupying more than 50% of the shoreline. Foredune erosion and retreat is occurring at an average rate of 0.8 m∙a−1. The marked differences in dune character between the west and east coasts

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17

Haddad, Wassim M., VijaySekhar Chellaboina, Qing Hui, and Sergey Nersesov. "Vector dissipativity theory for large-scale impulsive dynamical systems." Mathematical Problems in Engineering 2004, no. 3 (2004): 225–62. http://dx.doi.org/10.1155/s1024123x04310021.

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Modern complex large-scale impulsive systems involve multiple modes of operation placing stringent demands on controller analysis of increasing complexity. In analyzing these large-scale systems, it is often desirable to treat the overall impulsive system as a collection of interconnected impulsive subsystems. Solution properties of the large-scale impulsive system are then deduced from the solution properties of the individual impulsive subsystems and the nature of the impulsive system interconnections. In this paper, we develop vector dissipativity theory for large-scale impulsive dynamical

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18

Wang, Fengling, and Boling Guo. "Enlarged evolution system of measures of stochastic p-Laplace lattice systems with superlinear noise." Nonlinearity 38, no. 4 (2025): 045005. https://doi.org/10.1088/1361-6544/adbb49.

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Abstract This paper deals with the stochastic p-Laplace lattice systems driven by superlinear noise on Banach space ℓ p (an enlarged optimized space compared to Hilbert space ℓ 2 ) with p > 2. We use the dissipativeness of the nonlinear drift term growing at a polynomial growth rate p to control the superlinear noise, whose coefficient grows at a polynomial growth order q ∈ [ 2 , p ) . Thereby we show that the existence and uniqueness of enlarged solutions in C ( [ τ , ∞ ) , L p ( Ω , ℓ p ) ) ∩ L 2 p − 2 ( Ω , L loc 2 p − 2 ( τ , ∞ ; ℓ 2 p − 2 ) ) , and thus the existence of enlarged mean w

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19

Anshu, Balram Dubey, Sourav Kumar Sasmal, and Anand Sudarshan. "Consequences of fear effect and prey refuge on the Turing patterns in a delayed predator–prey system." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 12 (2022): 123132. http://dx.doi.org/10.1063/5.0126782.

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This study presents a qualitative analysis of a modified Leslie–Gower prey–predator model with fear effect and prey refuge in the presence of diffusion and time delay. For the non-delayed temporal system, we examined the dissipativeness and persistence of the solutions. The existence of equilibria and stability analysis is performed to comprehend the complex behavior of the proposed model. Bifurcation of codimension-1, such as Hopf-bifurcation and saddle-node, is investigated. In addition, it is observed that increasing the strength of fear may induce periodic oscillations, and a higher value

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20

Khalatur, Svitlana, Oksana Honcharenko, Oleksandr Karamushka, Ilona Solodovnykova, and Inna Shramko. "PARADIGM TRANSFORMATION OF THE ECONOMIC CRISES MODELING." Financial and credit activity problems of theory and practice 4, no. 45 (2022): 285–97. http://dx.doi.org/10.55643/fcaptp.4.45.2022.3833.

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In order to develop reasonable measures to counteract the destructive consequences of economic crises or to prevent them, it is important to build reasonable and adequate models of the emergence and course of crisis processes. The formal compliance of existing models with socio-economic processes during the crisis is often incomplete or cannot be adapted to other conditions, economies, and markets. Therefore, the article is devoted to the expediency and possibility of transformation of the existing paradigm of modeling economic crises.Modeling the interdependence of two basic indicators, which

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21

León, Iván, and Diego Pazó. "Dynamics and chaotic properties of the fully disordered Kuramoto model." Chaos: An Interdisciplinary Journal of Nonlinear Science 35, no. 7 (2025). https://doi.org/10.1063/5.0272051.

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Frustrated random interactions are a key ingredient of spin glasses. From this perspective, we study the dynamics of the Kuramoto model with quenched random couplings: the simplest oscillator ensemble with fully disordered interactions. We answer some open questions by means of extensive numerical simulations and a perturbative calculation (the cavity method). We show that frequency entrainment is not realized in the thermodynamic limit and that chaotic dynamics are pervasive in parameter space. In the weak coupling regime, we find closed formulas for the frequency shift and the dissipativenes

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22

Sakthivel, R., R. Mohana Priya, Chao Wang, and P. Dhanalakshmi. "Observer-Based Finite-Time Nonfragile Control for Nonlinear Systems With Actuator Saturation." Journal of Computational and Nonlinear Dynamics 14, no. 1 (2018). http://dx.doi.org/10.1115/1.4041911.

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This paper considers a design problem of dissipative and observer-based finite-time nonfragile control for a class of uncertain discrete-time system with time-varying delay, nonlinearities, external disturbances, and actuator saturation. In particular, in this work, it is assumed that the nonlinearities satisfy Lipschitz condition for obtaining the required results. By choosing a suitable Lyapunov–Krasovskii functional, a new set of sufficient conditions is obtained in terms of linear matrix inequalities, which ensures the finite-time boundedness and dissipativeness of the resulting closed-loo

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23

Caraballo, Tomás, Boling Guo, Nguyen Huy Tuan, and Renhai Wang. "Asymptotically autonomous robustness of random attractors for a class of weakly dissipative stochastic wave equations on unbounded domains." Proceedings of the Royal Society of Edinburgh: Section A Mathematics, November 5, 2020, 1–31. http://dx.doi.org/10.1017/prm.2020.77.

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This paper is concerned with the asymptotic behaviour of solutions to a class of non-autonomous stochastic nonlinear wave equations with dispersive and viscosity dissipative terms driven by operator-type noise defined on the entire space $\mathbb {R}^n$ . The existence, uniqueness, time-semi-uniform compactness and asymptotically autonomous robustness of pullback random attractors are proved in $H^1(\mathbb {R}^n)\times H^1(\mathbb {R}^n)$ when the growth rate of the nonlinearity has a subcritical range, the density of the noise is suitably controllable, and the time-dependent force converges

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24

Guo, Ke, and Songbai Guo. "Lyapunov functionals for a general time-delayed virus dynamic model with different CTL responses." Chaos: An Interdisciplinary Journal of Nonlinear Science 34, no. 5 (2024). http://dx.doi.org/10.1063/5.0204169.

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A time-delayed virus dynamic model is proposed with general monotonic incidence, different nonlinear CTL (cytotoxic T lymphocyte) responses [CTL elimination function pyg1(z) and CTL stimulation function cyg2(z)], and immune impairment. Indeed, the different CTL responses pose challenges in obtaining the dissipativeness of the model. By constructing appropriate Lyapunov functionals with some detailed analysis techniques, the global stability results of all equilibria of the model are obtained. By the way, we point out that the partial derivative fv(x,0) is increasing (but not necessarily strict

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25

Xu, Ling, Jianhua Huang, and Qiaozhen Ma. "Random attractors for the stochastic coupled suspension bridge equations of Kirchhoff type." Advances in Difference Equations 2019, no. 1 (2019). http://dx.doi.org/10.1186/s13662-019-2346-3.

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Abstract This paper is devoted to the dynamical behavior of stochastic coupled suspension bridge equations of Kirchhoff type. For the deterministic cases, there are many classical results such as existence and uniqueness of a solution and long-term behavior of solutions. To the best of our knowledge, the existence of random attractors for the stochastic coupled suspension bridge equations of Kirchhoff type is not yet considered. We intend to investigate these problems. We first obtain the dissipativeness of a solution in higher-energy spaces $H^{3}(U)\times H_{0}^{1}(U)\times (H^{2}(U)\cap H_{

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26

Sardar, Purnendu, Krishna Pada Das, Santosh Biswas, and Sourav Rana. "Impact of Honest Signal, Cues, Prey’s Experience Rate and Environmental Toxicity in a Predator–Prey Interaction Model." Biophysical Reviews and Letters, November 12, 2024, 1–31. http://dx.doi.org/10.1142/s1793048024500085.

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Biological signaling plays a crucial role in predator–prey interaction systems, serving both intraspecific and interspecific communication purposes. Prey populations utilize signaling internally, employing honest signals among themselves to enhance their defense capabilities. Conversely, they also use signaling for interspecific communication, emitting cues to predators to increase their own chances of survival. Recently, Al-Salman et al. [Appl. Math. Modell. 89, 1405 (2021)] proposed a two-species interaction model incorporating Holling Type II predation along with honest signals and cues. In

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27

Bozzeda, Fabio, Leonardo Ortega, Leonardo Lopes Costa, et al. "Global patterns in sandy beach erosion: unraveling the roles of anthropogenic, climatic and morphodynamic factors." Frontiers in Marine Science 10 (October 9, 2023). http://dx.doi.org/10.3389/fmars.2023.1270490.

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Beach erosion is a complex process influenced by multiple factors operating at different spatial scales. Local (e.g., waves, tides, grain size, beach width and coastal development) and regional (e.g., sea level rise and mean sea level pressure) factors both shape erosion processes. A comprehensive understanding of how these drivers collectively impact sandy beach erosion is needed. To address this on a global-scale we assembled a database with in-situ information on key physical variables from 315 sandy beaches covering a wide morphodynamic range and complemented by satellite data on regional

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28

Sieriebriak, Kseniia, Ivan Bodnia, and Ivan Kerezvas. "CHARACTERISTICS AND PROPERTIES OF THE INSTITUTIONAL ENVIRONMENT OF INNOVATIVE DEVELOPMENT OF ENTERPRISES IN THE REGION." Business Navigator, no. 2(72) (2023). http://dx.doi.org/10.32782/business-navigator.72-12.

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It is proven that regional innovation systems can be studied as a set of institutions whose activities are aimed at creating and spreading knowledge, technologies and innovations. On the one hand, regional innovation systems are considered as a set of organizations and enterprises that carry out activities for the creation, commercialization, promotion and diffusion of innovations, as a set of infrastructural elements that ensure innovation processes. On the other hand, regional innovation systems can be studied as a set of institutions whose activities are aimed at creating and spreading know

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