Existence and asymptotic behavior results of periodic solution for discrete-time neutral-type neural networks

Du, Bo; Liu, Yurong; Abbas, Ibrahim A.

doi:10.1016/j.jfranklin.2015.11.013

Cited by 52 publications

(16 citation statements)

References 34 publications

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“…In order to investigate the dynamical characteristics with respect to digital signal transmission, it is essential to formulate the discrete analog of neural networks. In recent years, many researches have been obtained for the dynamic analysis of discrete-time determinant or stochastic neural networks formulated by Euler scheme [2,8,10,12,20,25,26,34].…”

Section: Introductionmentioning

confidence: 99%

Mean almost periodicity and moment exponential stability of discrete-time stochastic shunting inhibitory cellular neural networks with time delays

Zhang¹,

Xu²

2019

Kybernetika

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Section: Introductionmentioning

confidence: 99%

Mean almost periodicity and moment exponential stability of discrete-time stochastic shunting inhibitory cellular neural networks with time delays

Zhang¹,

Xu²

2019

Kybernetika

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“…For proving the global exponential stability of periodic solutions of system (1), we only need to prove the global exponential stability of periodic solutions of system (2). Lemma 2.3 (Lemma 2.1 [40]) If |c n | < 1, n = 1, 2, . .…”

Section: Definition 21 (Graph Theorymentioning

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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“…Thus, neutral‐type neural networks with D operator have more realistic significance than non‐operator‐based ones in many practical applications of neural networks dynamics. Based on the complex neural reactions, neutral‐type neural networks with D operator can be described by the neutral‐type functional differential equation, for more details, we refer the readers to References . For example, using exponential dichotomy theory, contraction mapping principle and discrete‐continuous analysis method, Du et al studied the almost periodic solution for the following neutral‐type neural networks with distributed leakage delays on time scales of the form:

\begin{align} ({, \begin{matrix} left left \\ array {(A_{i} x_{i})}^{\nabla} (t) & array = - a_{i} (t) \int_{0}^{+ \infty} k_{i} (s) x_{i} (t - s) \nabla s + \sum_{j = 1}^{n} b_{i j} (t) f_{j} (x_{j} (t)) \\ array + \sum_{j = 1}^{n} d_{i j} (t) g_{j} (x_{j} (t - τ_{i j} (t))) + I_{i} (t), \\ array x_{i} (t) & array = φ_{i} (t), t \in {(- \infty, 0]}_{T}, i = 1, 2, \dots, n, \end{matrix}) \end{align}

…”

Section: Introductionmentioning

confidence: 99%

Antiperiodic dynamical behaviors of discontinuous neutral‐type Cohen‐Grossberg neural networks with mixed time delays

Kong

Zhu

2019

Computational Intelligence

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This article presents a class of neutral‐type Cohen‐Grossberg neural networks with discontinuous activations and mixed time delays. Based on the functional differential inclusions theory, inequality technique, and nonsmooth analysis theory with Lyapunovlike approach, some new sufficient criteria are given to ascertain the existence, uniqueness, and globally exponential stability of the antiperiodic solution. Finally, two topical numerical examples and the corresponding computer simulations are delineated to substantiate the correctness of our theoretical predictions. The obtained results of this article are new and complement some related earlier works.

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Existence and asymptotic behavior results of periodic solution for discrete-time neutral-type neural networks

Cited by 52 publications

References 34 publications

Mean almost periodicity and moment exponential stability of discrete-time stochastic shunting inhibitory cellular neural networks with time delays

Mean almost periodicity and moment exponential stability of discrete-time stochastic shunting inhibitory cellular neural networks with time delays

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

Antiperiodic dynamical behaviors of discontinuous neutral‐type Cohen‐Grossberg neural networks with mixed time delays

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