Dynamical behavior of reaction–diffusion neural networks and their synchronization arising in modeling epileptic seizure: A numerical simulation study

Moayeri, Mohammad Mahdi; Rad, Jamal Amani; Parand, Kourosh

doi:10.1016/j.camwa.2020.08.020

Cited by 13 publications

(2 citation statements)

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“…Suppose that assumptions (H 1 ) and (H 2 ) hold. Then, the equilibrium point Y * = (x * , s * ) T of system ( 16) is globally asymptotically stable under the initial conditions (17) and (18), provided that…”

Section: Ds < ∞;mentioning

confidence: 99%

“…Zheng et al [16] considered the fixed-time synchronization of discontinuous competitive neural networks. Dynamical behavior of reaction-diffusion neural networks and their synchronization was considered in [17]. For state estimation for delayed genetic regulatory networks with reaction-diffusion terms, see [18]; for stability and asymptotic stability problems for neural networks with reaction-diffusion terms, see [19,20]; and for oscillatory behaviors for neural networks with reaction-diffusion terms, see [21,22].…”

Section: Introductionmentioning

confidence: 99%

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Global Asymptotic Stability of Competitive Neural Networks with Reaction-Diffusion Terms and Mixed Delays

Shao¹,

2022

Symmetry

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In this article, a new competitive neural network (CNN) with reaction-diffusion terms and mixed delays is proposed. Because this network system contains reaction-diffusion terms, it belongs to a partial differential system, which is different from the existing classic CNNs. First, taking into account the spatial diffusion effect, we introduce spatial diffusion for CNNs. Furthermore, since the time delay has an essential influence on the properties of the system, we introduce mixed delays including time-varying discrete delays and distributed delays for CNNs. By constructing suitable Lyapunov–Krasovskii functionals and virtue of the theories of delayed partial differential equations, we study the global asymptotic stability for the considered system. The effectiveness and correctness of the proposed CNN model with reaction-diffusion terms and mixed delays are verified by an example. Finally, some discussion and conclusions for recent developments of CNNs are given.

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Section: Ds < ∞;mentioning

confidence: 99%