Stability of Reaction-Diffusion Recurrent Neural Networks with Distributed Delays and Neumann Boundary Conditions on Time Scales

Zhao, Kaihong; Ye, Yuan

doi:10.1007/s11063-012-9232-2

Cited by 7 publications

(5 citation statements)

References 29 publications

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“…Recent related studies have shown that time scales are not only a theoretical territory of mathematics, but also an efective tool to handle many practical matters [17][18][19][20]. Although extensive research has been conducted on the stability analysis of dynamic equations on time scales, most of them were limited to ordinary diferential equations, and few studies on the stability of PDEs on time scales were made [21][22][23]. To overcome this shortcoming, this study examines the stability of the second-order linear PDEs on time scales based on the Lyapunov functional method.…”

Section: Introductionmentioning

confidence: 99%

“…(1) Compared to the existing works [21][22][23], the PDEs under consideration is more general for that where both the difusion operator and second-order partial diferential terms are taking into account. (2) Based on the Lyapunov functional and inequality methods, the sufcient conditions of stability are presented, and the results are generalized that they can unify the continuous-time and discrete-time cases.…”

Section: Introductionmentioning

confidence: 99%

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Stability Analysis of Second-Order Linear PDEs on Time Scales

Liu

Zhang

et al. 2023

Discrete Dynamics in Nature and Society

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This paper presents the stability analysis of a class of second-order linear partial differential equations (PDEs) on time scales with diffusion operator and first-order partial derivative. According to the time scale theory, the Lyapunov functional method, and some inequality techniques, sufficient conditions for exponential stability are strictly obtained, and the results are generalized for that where both the discrete-time and continuous-time cases are considered jointly. In addition, the theoretical results are applied to exponential synchronization of reaction-diffusion neural networks (RDNNs). Simulation examples are given to verify the feasibility of our results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Second-Order Linear PDEs on Time Scales

Liu

Zhang

et al. 2023

Discrete Dynamics in Nature and Society

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“…In the past three decades, the cellular neural networks (CNNs) have gained a lot of popularity due to their local inter-connectivity and practical hardware implementation [1][2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Stability analysis for periodic solutions of fuzzy shunting inhibitory CNNs with delays

2019

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We consider fuzzy shunting inhibitory cellular neural networks (FSICNNs) with time-varying coefficients and constant delays. By virtue of continuation theorem of coincidence degree theory and Cauchy-Schwartz inequality, we prove the existence of periodic solutions for FSICNNs. Furthermore, by employing a suitable Lyapunov functional we establish sufficient criteria which ensure global exponential stability of the periodic solutions. Numerical simulations that support the theoretical discussions are depicted.

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“…To avoid the troublesomeness of studying the dynamical properties for continuous and discrete systems, respectively, it is meaningful to study that on time scales, which was initiated by Stefan Hilger in his Ph.D. thesis in order to unify continuous and discrete analysis. Lots of scholars have studied neural networks on time scales and obtained many good results [23][24][25][26][27][28][29]. For example, in [30], the authors considered the existence and global exponential stability of an equilibrium point for a class of fuzzy BAM neural networks with time-varying delays in leakage terms on time scales.…”

Section: Introductionmentioning

confidence: 99%

Existence and Exponential Stability of Equilibrium Point for Fuzzy BAM Neural Networks with Infinitely Distributed Delays and Impulses on Time Scales

Sun

Yang

2014

Journal of Applied Mathematics

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By using the fixed point theorem and constructing a Lyapunov functional, we establish some sufficient conditions on the existence, uniqueness, and exponential stability of equilibrium point for a class of fuzzy BAM neural networks with infinitely distributed delays and impulses on time scales. We also present a numerical example to show the feasibility of obtained results. Our example also shows that the described time and continuous neural time networks have the same dynamic behaviours for the stability.

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Stability of Reaction-Diffusion Recurrent Neural Networks with Distributed Delays and Neumann Boundary Conditions on Time Scales

Cited by 7 publications

References 29 publications

Stability Analysis of Second-Order Linear PDEs on Time Scales

Stability Analysis of Second-Order Linear PDEs on Time Scales

Stability analysis for periodic solutions of fuzzy shunting inhibitory CNNs with delays

Existence and Exponential Stability of Equilibrium Point for Fuzzy BAM Neural Networks with Infinitely Distributed Delays and Impulses on Time Scales

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