Non-typical multistability in neural networks with distributed delays

Cheng, Chang-Yuan

doi:10.1016/j.neucom.2013.04.022

Cited by 6 publications

(2 citation statements)

References 29 publications

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“…So, by Definition 2 and inequality (10) and (13), networks (1) are globally exponentially stable in Lagrange sense. Therefore, the conclusion holds and the proof is completed.…”

Section: Proof Consider Lyapunov Function As Followsmentioning

confidence: 99%

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Exponential convergence and Lagrange stability for impulsive Cohen–Grossberg neural networks with time-varying delays

Jian

2015

Journal of Computational and Applied Mathematics

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h i g h l i g h t s• We discuss Lagrange stability for impulsive Cohen-Grossberg neural networks.• We establish a new delay impulsive differential inequality. • Some easily verified conditions of Lagrange exponential stability are obtained.• Giving out the detail estimations of the exponential convergence ball.• The results here generalize and improve the earlier publications. a b s t r a c tIn this paper, the problem on exponential convergence and Lagrange exponential stability for a class of delayed Cohen-Grossberg neural networks with impulses effects is investigated. To this end, a new delay impulsive differential inequality is established, which improves and generalizes previously known criteria. By using the new inequality and coupling with the Lyapunov method, several sufficient conditions are derived to guarantee the global exponential stability in Lagrange sense and exponential convergence of the state variables of the discussed delayed Cohen-Grossberg neural networks with impulses effects. Meanwhile, the framework of the exponential convergence ball in the state space with a pre-specified convergence rate is also given. Here, the existence and uniqueness of the equilibrium points need not to be considered. Finally, some numerical examples with simulation show the effectiveness of the obtained results.

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“…So, by Definition 2 and inequality (10) and (13), networks (1) are globally exponentially stable in Lagrange sense. Therefore, the conclusion holds and the proof is completed.…”

Section: Proof Consider Lyapunov Function As Followsmentioning

confidence: 99%

“…Many research results on multistability of neural networks have been reported by [9][10][11][12][13][14], these dynamics maybe have multiple equilibrium and so many of them are unstable [11,12]. In [13,14], the authors considered the multistability for impulsive hybrid Hopfield neural networks and discrete-time Hopfield neural networks.…”

Section: Introductionmentioning

confidence: 99%