Existence and global exponential stability of periodic solutions for coupled control systems on networks with feedback and time delays

Gao, Shang; Wang, Qi; Wu, Boying

doi:10.1016/j.cnsns.2018.03.012

Cited by 9 publications

(2 citation statements)

References 30 publications

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“…This is why stabilization of the neural networks has recently attracted wide audience and witnessed day-to-day growing investigations. In this way, the interested follower is advised to study the following papers: [ 9 , 10 , 13 , 15 , 17 – 23 , 26 – 44 ]. For convenience let us make a convention here.…”

Section: Introductionmentioning

confidence: 99%

Existence and global asymptotic stability criteria for nonlinear neutral-type neural networks involving multiple time delays using a quadratic-integral Lyapunov functional

Gholami

2021

Adv Differ Equ

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In this paper we consider a standard class of the neural networks and propose an investigation of the global asymptotic stability of these neural systems. The main aim of this investigation is to define a novel Lyapunov functional having quadratic-integral form and use it to reach a stability criterion for the under study neural networks. Since some fundamental characteristics, such as nonlinearity, including time-delays and neutrality, help us design a more realistic and applicable model of neural systems, we will use all of these factors in our neural dynamical systems. At the end, some numerical simulations are presented to illustrate the obtained stability criterion and show the essential role of the time-delays in appearance of the oscillations and stability in the neural networks.

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Section: Introductionmentioning

confidence: 99%

Existence and global asymptotic stability criteria for nonlinear neutral-type neural networks involving multiple time delays using a quadratic-integral Lyapunov functional

Gholami

2021

Adv Differ Equ

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“…In recent years, graph theory has been applied to studying global asymptotic stability of discrete-time Cohen-Grossberg neural networks with finite and infinite delays [30] and the existence and global stability of periodic solutions for coupled networks [31][32][33][34][35]. Some sufficient conditions on the existence and global stability of equilibrium point and periodic solutions for some neural networks and coupled networks have been established [30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Periodic solutions for complex-valued neural networks of neutral type by combining graph theory with coincidence degree theory

Zhang

Cao

2018

Adv Differ Equ

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In this paper, by combining graph theory with coincidence degree theory as well as Lyapunov functional method, sufficient conditions to guarantee the existence and global exponential stability of periodic solutions of the complex-valued neural networks of neutral type are established. In our results, the assumption on the boundedness for the activation function in (Gao and Du in Discrete Dyn. Nat. Soc. 2016:Article ID 1267954, 2016) is removed and the other inequality conditions in (Gao and Du in Discrete Dyn. Nat. Soc. 2016:Article ID 1267954, 2016) are replaced with new inequalities.

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Novel Sufficient Conditions on Periodic Solutions for Discrete-Time Neutral-Type Neural Networks

Zhou

Zhang

2019

Neural Process Lett

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Existence and global exponential stability of periodic solutions for coupled control systems on networks with feedback and time delays

Cited by 9 publications

References 30 publications

Existence and global asymptotic stability criteria for nonlinear neutral-type neural networks involving multiple time delays using a quadratic-integral Lyapunov functional

Existence and global asymptotic stability criteria for nonlinear neutral-type neural networks involving multiple time delays using a quadratic-integral Lyapunov functional

Periodic solutions for complex-valued neural networks of neutral type by combining graph theory with coincidence degree theory

Novel Sufficient Conditions on Periodic Solutions for Discrete-Time Neutral-Type Neural Networks

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