Anti-periodic solution for impulsive BAM neural networks with time-varying leakage delays on time scales

Yang, Li; Wu, Wenqi

doi:10.1016/j.neucom.2014.08.020

Cited by 46 publications

(16 citation statements)

References 40 publications

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“…Some authors argue that a typical time delay called Leakage (or 'forgetting') delay may occur in the negative feedback term of the neural networks model (these terms are variously known as forgetting or leakage terms) and has a great impact on the dynamics of neural networks [19][20][21][22][23][24][25][26][27][28]. For example, time delay in the stabilizing negative feedback term has a tendency to destabilize a system [29], Li et al [30]pointed out that the existence and uniqueness of the equilibrium point are independent of time delays and initial conditions.…”

Section: Introductionmentioning

confidence: 99%

Existence and exponential stability of almost periodic solutions for neutral‐type BAM neural networks with distributed leakage delays

Pang

2016

Math Methods in App Sciences

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This paper is concerned with a class of neutral‐type BAM neural networks with distributed leakage delays. By applying the exponential dichotomy of linear differential equations, Lyapunov functional method and contraction mapping principle, we establish some sufficient conditions which ensure the existence and exponential stability of almost periodic solutions for such BAM neural networks. An example is given to illustrate the effectiveness of the theoretical findings. The results obtained in this article are completely new and complement the previously known studies. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

Existence and exponential stability of almost periodic solutions for neutral‐type BAM neural networks with distributed leakage delays

Pang

2016

Math Methods in App Sciences

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“…So, in order to analyze the dynamical behaviors to neural networks, incorporating time delays and impulsive effects into them is a nature and necessary step. Numerous results on impulsive effects have been gained for delayed neural networks, see previous studies() and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Existence and global exponential stability of anti‐periodic solutions for delayed quaternion‐valued cellular neural networks with impulsive effects

Qin

2018

Math Methods in App Sciences

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In this paper, we consider a class of delayed quaternion-valued cellular neural networks (DQVCNNs) with impulsive effects. By using a novel continuation theorem of coincidence degree theory, the existence of anti-periodic solutions for DQVCNNs is obtained with or without assuming that the activation functions are bounded. Furthermore, by constructing a suitable Lyapunov function, some sufficient conditions are derived to guarantee the global exponential stability of anti-periodic solutions for DQVCNNs. Our results are new and complementary to the known results even when DQVCNNs degenerate into real-valued or complex-valued neural networks. Finally, an example is given to illustrate the effectiveness of the obtained results. KEYWORDSanti-periodic solution, neural networks, quaternion, stabilitywhere q 0 , q 1 , q 2 , q 3 are real numbers and the elements i, j, and k obey the Hamilton's multiplication rules:In the past two decades, the theory of quaternion has been found a lot of applications in many fields such as such as attitude control, quantum mechanics, robotics, computer graphics, and so on. 26-30 Quaternion-valued neural networks (QVNNs), Math Meth Appl Sci. 2019;42:5-23.wileyonlinelibrary.com/journal/mma

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“…Therefore, many authors have studied the dynamical behaviors of neural networks on time scales for recent years (see Ref. [9][10][11][12][13][16][17] and reference therein).…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, the neural networks are often subject to abrupt changes at certain moments due to instantaneous perturbations which lead to impulsive effects. Since the existence of impulses is frequently a source of instability, bifurcation and chaos for neural networks, the impulsive neural networks are an appropriate description of the phenomena of abrupt qualitative dynamical changes of essentially continuoustime system (see [15][16][17][18] and reference therein). Hence, it is very meaningful to investigate almost periodic dynamics for impulsive BAM neural networks with variable delays and continuously distributed delays on almost periodic time scales.…”

Section: Introductionmentioning

confidence: 99%

Existence and Exponential Stability of Almost Periodic Solutions for Impulsive BAM Neural Networks on Almost Periodic Time Scales

Chen¹,

Xu²

2017

dtcse

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This paper considers almost periodic dynamics for impulsive BAM neural networks with variable delays and continuously distributed delays on almost periodic time scales. By applying contraction principle and Gromwell-Bellman's inequality, some new results on the existence and exponential stability of almost periodic solutions are established. In addition, an example is provided to illustrate the feasibility and effectiveness of the obtained results.

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Anti-periodic solution for impulsive BAM neural networks with time-varying leakage delays on time scales

Cited by 46 publications

References 40 publications

Existence and exponential stability of almost periodic solutions for neutral‐type BAM neural networks with distributed leakage delays

Existence and exponential stability of almost periodic solutions for neutral‐type BAM neural networks with distributed leakage delays

Existence and global exponential stability of anti‐periodic solutions for delayed quaternion‐valued cellular neural networks with impulsive effects

Existence and Exponential Stability of Almost Periodic Solutions for Impulsive BAM Neural Networks on Almost Periodic Time Scales

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