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

Zhang, Tianwei; Xu, Li

doi:10.14736/kyb-2019-4-0690

Cited by 5 publications

(14 citation statements)

References 45 publications

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“…Remark 2. According to equation ( 8), the authors 7,[31][32][33][34] studied the dynamic behaviors of different forms of discrete applied models, for example, almost periodic dynamics, 7,31,33 stochastic perturbations 7,32,33 and stability. 34 Obviously, equation (3) of this article is an expansion of discrete analogues in literature.…”

Section: Mittag-leffler Euler Discrete Analoguementioning

confidence: 99%

“…By employing exponential Euler differences like equation ( 8), literatures 7,31,33,34 discussed the periodicity, almost periodicity and stability of discrete models. Zhang and Xu 7 discussed mean almost periodic dynamics to exponential Euler discrete shunting inhibitory cellular neural networks with the same difference technique. Thus, the work of this article supplements and extends the corresponding results in papers.…”

Section: Theorem 3 Equation (M) Has the Property Of Exponential Stabi...mentioning

confidence: 99%

“…Thus, the work of this article supplements and extends the corresponding results in papers. 7,31,33,34 Remark 8. In allusion to continuous-time fractionalorder neural networks with time lags, it is difficult to discuss the exponential stability and numerous literatures focus on Mittag-Leffler stability or global asymptotic stability.…”

Section: Theorem 3 Equation (M) Has the Property Of Exponential Stabi...mentioning

confidence: 99%

“…(5) The research findings in this article extend and complement the works in literatures. 7,[31][32][33][34] (6) The work of this article starts the study of Mittag-Leffler discrete shunting inhibitory cellular neural networks and the theories and methods can be applied to the study of other fractional-order models.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Equilibrium point, exponential stability and synchronization of numerical fractional-order shunting inhibitory cellular neural networks with piecewise feature

Luo

Zhang

2022

Proceedings of the Institution of Mechanical Engineers, Part I:

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In recent years, exponential Euler difference methods for first-order semi-linear differential equations have been developed rapidly, and various exponential Euler difference methods have become a very important research topic. For fractional-order shunting inhibitory cellular neural networks with time lags, this article first establishes a new difference method named Mittag-Leffler Euler difference, which includes exponential Euler difference. Second, the existence of unique global bounded solution and equilibrium point, exponential stability and synchronization of the derived difference model are investigated. Compared with the classical fractional-order Euler difference method, the Mittag-Leffler discrete shunting inhibitory cellular neural networks can better describe and maintain the dynamic properties of the corresponding continuous-time models. More importantly, it opens up a new way to study discrete-time fractional-order systems and establishes a set of theory and methods to study Mittag-Leffler discrete neural networks.

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Section: Mittag-leffler Euler Discrete Analoguementioning

confidence: 99%

Section: Theorem 3 Equation (M) Has the Property Of Exponential Stabi...mentioning

confidence: 99%

Section: Theorem 3 Equation (M) Has the Property Of Exponential Stabi...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Equilibrium point, exponential stability and synchronization of numerical fractional-order shunting inhibitory cellular neural networks with piecewise feature

Luo

Zhang

2022

Proceedings of the Institution of Mechanical Engineers, Part I:

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show abstract

“…Hence, if we consider the effects of the environmental factors, almost periodicity is more realistic and more general than periodicity. In recent years, the almost periodic solutions of the continuous models in biological populations 9, 10 and engineering areas 11 have been studied extensively.…”

Section: Introductionmentioning

confidence: 99%

Multiplicity of almost periodic oscillations in delayed harvesting predator-prey model with modified Leslie-Gower Holling-type II schemes

Zhang¹,

Han²

2019

ScienceAsia

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By means of a fixed point theorem of coincidence degree theory, sufficient conditions for the multiplicity of positive almost periodic solutions to a delayed harvesting predator-prey model with modified Leslie-Gower Hollingtype II schemes are established. The method used in this paper provides a possible method to study the multiplicity of positive almost periodic solutions of the models in biological populations. Finally, an example and computer simulations are given to illustrate the feasibility and effectiveness of our main results.

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Asymptotically almost periodic synchronization in fuzzy competitive neural networks with Caputo-Fabrizio operator

Zhang,

Qu,

Zhou

2023

Fuzzy Sets and Systems

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

Abstract: Tianwei Zhang; Lijun Xu Mean almost periodicity and moment exponential stability of discrete-time stochastic shunting inhibitory cellular neural networks with time delays

Cited by 5 publications

References 45 publications

Equilibrium point, exponential stability and synchronization of numerical fractional-order shunting inhibitory cellular neural networks with piecewise feature

Equilibrium point, exponential stability and synchronization of numerical fractional-order shunting inhibitory cellular neural networks with piecewise feature

Multiplicity of almost periodic oscillations in delayed harvesting predator-prey model with modified Leslie-Gower Holling-type II schemes

Asymptotically almost periodic synchronization in fuzzy competitive neural networks with Caputo-Fabrizio operator

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