Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

Zhang, Qianhong; Yang, Lei; Liao, Daixi

doi:10.2478/v10006-011-0051-9

Cited by 8 publications

(4 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Secondly, compared with continuous-time models, the advantage they offer is that they are generally more direct, more convenient and more accurate to formulate. Thirdly, recent works have shown that for discrete-time models the dynamics can produce a much richer set of patterns than those observed in continuous-time models (Busłowicz, 2010;Busłowicz and Ruszewski, 2012;Duda, 2012;Feedman, 1980;Holling, 1965;Huang and Xiao, 2004;Hsu, 1978;Raja et al, 2011;Xu et al, 2011;Zhang et al, 2011). At last, we can get more interesting dynamical behaviors and more accurate numerical simulations results from the discrete-time models; moreover, numerical simulations of continuous-time models are obtained by discretizing the models.…”

Section: Introductionmentioning

confidence: 98%

Bifurcation and control for a discrete-time prey–predator model with Holling-IV functional response

Chen¹,

Teng²,

Hu³

2013

International Journal of Applied Mathematics and Computer Science

View full text Add to dashboard Cite

The dynamics of a discrete-time predator-prey model with Holling-IV functional response are investigated. It is shown that the model undergoes a flip bifurcation, a Hopf bifurcation and a saddle-node bifurcation by using the center manifold theorem and bifurcation theory. Numerical simulations not only exhibit our results with the theoretical analysis, but also show the complex dynamical behaviors, such as the period-3, 6, 9, 12, 20, 63, 70, 112 orbits, a cascade of period-doubling bifurcations in period-2, 4, 8, 16, quasi-periodic orbits, an attracting invariant circle, an inverse period-doubling bifurcation from the period-32 orbit leading to chaos and a boundary crisis, a sudden onset of chaos and a sudden disappearance of the chaotic dynamics, attracting chaotic sets and non-attracting sets. We also observe that when the prey is in chaotic dynamics the predator can tend to extinction or to a stable equilibrium. Specifically, we stabilize the chaotic orbits at an unstable fixed point by using OGY chaotic control.

show abstract

Section: Introductionmentioning

confidence: 98%

Bifurcation and control for a discrete-time prey–predator model with Holling-IV functional response

Chen¹,

Teng²,

Hu³

2013

International Journal of Applied Mathematics and Computer Science

View full text Add to dashboard Cite

show abstract

“…So, it is of prime importance to consider the delay effects on the dynamical behavior of systems. Recently, FCNNs with various types of delay have been widely investigated by many authors; see [8][9][10][11][12] and references therein. However, so far, there has been very little existing work on FCNNs with time delay in the leakage (or ''forgetting'') term [13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Asymptotical state estimation of fuzzy cellular neural networks with time delay in the leakage term and mixed delays: Sample-data approach

Kalpana

Balasubramaniam

2016

Journal of the Egyptian Mathematical Society

View full text Add to dashboard Cite

In this paper, the sampled measurement is used to estimate the neuron states, instead of the continuous measurement, and a sampled-data estimator is constructed. Leakage delay is used to unstable the neuron states. It is a challenging task to develop delay dependent condition to estimate the unstable neuron states through available sampled output measurements such that the error-state system is globally asymptotically stable. By constructing Lyapunov-Krasovskii functional (LKF), a sufficient condition depending on the sampling period is obtained in terms of linear matrix inequalities (LMIs). Moreover, by using the free-weighting matrices method, simple and efficient criterion is derived in terms of LMIs for estimation. 2010 MATHEMATICS SUBJECT CLASSIFICATION: 03B52; 92B20; 93C57; 93D20 ª 2015 Production and hosting by Elsevier B.V. on behalf of Egyptian Mathematical Society.

show abstract

“…Such applications heavily depend on the dynamical behavior of the neural networks. Therefore the stability analysis of neural networks is a prerequisite for the applications and the problem of stability issues for recurrent neural networks has attracted considerable attention in recent years, see [4,17,27,28,34,36].…”

Section: Introductionmentioning

confidence: 99%

Exponential stability for stochastic delayed recurrent neural networks with mixed time-varying delays and impulses: the continuous-time case

Raja

Samidurai

et al. 2013

Phys. Scr.

View full text Add to dashboard Cite

In this paper, the exponential stability for a class of stochastic neural networks with time-varying delays and impulsive effects is considered. By constructing suitable Lyapunov functionals and by using the linear matrix inequality optimization approach, we obtain sufficient delay-dependent criteria to ensure the exponential stability of stochastic neural networks with time-varying delays and impulses. Two numerical examples with simulation results are provided to illustrate the effectiveness of the obtained results over those already existing in the literature.

show abstract

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

Cited by 8 publications

References 27 publications

Bifurcation and control for a discrete-time prey–predator model with Holling-IV functional response

Bifurcation and control for a discrete-time prey–predator model with Holling-IV functional response

Asymptotical state estimation of fuzzy cellular neural networks with time delay in the leakage term and mixed delays: Sample-data approach

Exponential stability for stochastic delayed recurrent neural networks with mixed time-varying delays and impulses: the continuous-time case

Contact Info

Product

Resources

About