Design of State-Dependent Switching Laws for Stability of Switched Stochastic Neural Networks With Time-Delays

Yang, Dan; Li, Xiaodi; Song, Shiji

doi:10.1109/tnnls.2019.2927161

Cited by 34 publications

(37 citation statements)

References 41 publications

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“…And so the system (2.1) possesses a unique positive bounded stationary solution y σ (x) for x ∈ Ω σ with y σ | ∂Ω σ = 0. Moreover, according to the proof of Theorem To show the idea of Remark 2, we may consider the stability of the constant equilibrium point of the following delayed reaction-diffusion Cohen-Grossberg neural networks which is the partial differential equations model studied in [2]: 19) where…”

Section: Resultsmentioning

confidence: 99%

Stability Analysis of Nontrivial Stationary Solution and Constant Equilibrium Point of Reaction-Diffusion Neural Networks with Time Delays under Dirichlet Zero Boundary Value

Rao¹

2020

Preprint

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In this paper, Lyapunov-Razumikhin technique, design of state-dependent switching laws, a fixed point theorem and variational methods are employed to derive the existence and the unique existence results of (globally) exponentially stable positive stationary solution of delayed reaction-diffusion cell neural networks under Dirichlet zero boundary value, including the global stability criteria \textbf{in the classical meaning}. Next, sufficient conditions are proposed to guarantee the global stability invariance of ordinary differential systems under the influence of diffusions. New theorems show that the diffusion is a double-edged sword in judging the stability of diffusion systems. Besides, an example is constructed to illuminate that any non-zero constant equilibrium point must be not in the phase plane of dynamic system under Dirichlet zero boundary value, or it must lead to a contradiction. Next, under Lipschitz assumptions on active function, another example is designed to prove that the small diffusion effect will cause the essential change of the phase plane structure of the dynamic behavior of the delayed neural networks via a Saddle point theorem. Finally, a numerical example illustrates the feasibility of the proposed methods.

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Section: Resultsmentioning

confidence: 99%

Stability Analysis of Nontrivial Stationary Solution and Constant Equilibrium Point of Reaction-Diffusion Neural Networks with Time Delays under Dirichlet Zero Boundary Value

Rao¹

2020

Preprint

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“…This illuminates that there are big differences between the stability criterion of the nontrivial stationary solution y * (x) and that of the constant equilibrium point y * . However, in previous related literature [1,2,15,16], for example, in [1], due to the poincare inequality or its other forms, there is completely similar between the stability criterion of the and that of its corresponding ordinary differential equations, we may consider the stability of the constant equilibrium point of the following delayed reaction-diffusion Cohen-Grossberg neural networks which is the partial differential equations model studied in [2]: 19) where all the variables, coefficients and functions are defined in [2], which are different from those of our Theorem 3.1. We always assume u i (t + k , x) = u i (t k , x).…”

Section: Resultsmentioning

confidence: 99%

Stability Analysis of Nontrivial Stationary Solution and Constant Equilibrium Point of Reaction-Diffusion Neural Networks With Time Delays

Rao¹

2020

Preprint

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Firstly, the existence of asymptotically stable nontrivial stationary solution is derived by the comprehensive applications of Lyapunov-Razumikhin technique, design of state-dependent switching laws, a fixed point theorem, variational methods, and construction of compact operators on a convex set. This new theorem shows that the diffusion is a double-edged sword to the stability, refuting the views in previous literature that the greater the diffusion effect, the more stable the system will be. Next, a series of new theorems are presented one by one, which illustrates that the globally asymptotical stability of ordinary differential equations model for delayed neural networks may be locally stable in actual operation due to the inevitable diffusion. Besides, the non-zero constant equilibrium point is pointed out to be not the solution of delayed reaction diffusion system so that the stability of the non-zero constant equilibrium point of reaction diffusion system must lead to a contradiction. That is, non-zero constant equilibrium points are not in the phase plane of dynamic system. In addition, new theorems are further presented to prove that the small diffusion effect will cause the essential change of the phase plane structure of the dynamic behavior of the delayed neural networks, and thereby one equilibrium solution may become several stationary solutions, even infinitely many positive stationary solutions. Finally, a numerical example illustrates the feasibility of the proposed methods.

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“…Moreover, due to the limited switching speed of neurons and amplifiers, time delays are inevitably introduced into biological and artificial neural network models. In recent years, the research on the dynamics of stochastic neural networks with time delays has become a hot topic [9]- [13].…”

Section: Introductionmentioning

confidence: 99%

Almost Periodic Solutions in Distribution Sense for Quaternion-Valued Stochastic Delayed Neural Networks

Meng

2020

IEEE Access

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In this paper, we consider quaternion-valued stochastic delayed neural networks. We first obtain the existence of almost periodic solutions in distribution sense by employing the contraction mapping principle. Then by using stochastic analysis and inequality techniques, we obtain the mean square global exponential stability of the almost periodic solutions of the considered neural networks. Finally, we present a numerical example to illustrate the feasibility of our results. INDEX TERMS Almost periodicity in distribution sense, mean square global exponential stability, quaternion-valued stochastic neural network.

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Design of State-Dependent Switching Laws for Stability of Switched Stochastic Neural Networks With Time-Delays

Cited by 34 publications

References 41 publications

Stability Analysis of Nontrivial Stationary Solution and Constant Equilibrium Point of Reaction-Diffusion Neural Networks with Time Delays under Dirichlet Zero Boundary Value

Stability Analysis of Nontrivial Stationary Solution and Constant Equilibrium Point of Reaction-Diffusion Neural Networks with Time Delays under Dirichlet Zero Boundary Value

Stability Analysis of Nontrivial Stationary Solution and Constant Equilibrium Point of Reaction-Diffusion Neural Networks With Time Delays

Almost Periodic Solutions in Distribution Sense for Quaternion-Valued Stochastic Delayed Neural Networks

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