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Neural Processing Letters
Erschienen in: Neural Processing Letters 2/2017

16.08.2016

Stability and Hopf Bifurcation of Time Fractional Cohen–Grossberg Neural Networks with Diffusion and Time Delays in Leakage Terms

verfasst von: Xiaohong Tian, Rui Xu

Erschienen in: Neural Processing Letters | Ausgabe 2/2017

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Abstract

In this paper, a class of time fractional Cohen–Grossberg neural networks with time delays in leakage terms and diffusion under homogeneous Neumann boundary conditions is investigated. By analyzing the corresponding characteristic equation, the local stability of the trivial uniform steady state and the existence of Hopf bifurcation are established. By using the normal form theory and the center manifold reduction of partial functional differential equations, explicit formulae are obtained to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main theoretical results.
Vorheriger Artikel One-Class Classification Based on Extreme Learning and Geometric Class Information
Nächster Artikel Piecewise Pseudo Almost Periodic Solution for Impulsive Generalised High-Order Hopfield Neural Networks with Leakage Delays

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Literatur
1.
Boroomand A, Menhaj MB (2009) Fractional-order Hopfield neural networks. Adv Neuro Inf Process 5506:883–890
2.
Boushaba K, Ruan S (2001) Instability in diffusive ecological models with nonlocal delay effects. J Math Anal Appl 258:269–286MathSciNetCrossRefMATH
3.
Chen L, Wu R, He Y et al (2015) Robust stability and stabilization of fractional-order linear systems with polytopic uncertainties. Appl Math Comput 257:274–284MathSciNetMATH
4.
Chen Z, Liu B (2013) Convergence behavior of Cohen–Grossberg neural networks with time-varying delays in the leakage terms. Neurocomputing 120:518–523CrossRef
5.
6.
Cohen M, Grossberg S (1983) Absolute stability and global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans Syst Man Cybern 13:815–826MathSciNetCrossRefMATH
7.
Deng W, Li C, Lü J (2007) Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn 48:409–416MathSciNetCrossRefMATH
8.
Faria T (2000) Normal forms and Hopf bifurcation for partial differential equations with delays. Trans Am Math Soc 352:2217–2238MathSciNetCrossRefMATH
9.
Gafiychuk V, Datsko B, Meleshko V (2008) Mathematical modeling of time fractional reaction-diffusion systems. J Comput Appl Math 220:215–225MathSciNetCrossRefMATH
10.
11.
Guo B, Pu X, Huang F (2015) Fractional partial differential equations and their numerical solutions. Science Press, BeijingCrossRefMATH
12.
13.
14.
Jin D, Huang Z, Peng J (2011) Approximation on attraction domain of Cohen–Grossberg neural networks. Appl Math Comput 217:8747–8753MathSciNetMATH
15.
Kaslik E, Sivasundaram S (2011) Dynamics of fractional-order neural networks. In: IEEE, Proceedings of the international conference on neural networks, California, pp 611–618
16.
Kao Y, Guo J, Wang C et al (2012) Delay-dependent robust exponential stability of Markovian jumping reaction-diffusion Cohen–Grossberg neural networks with mixed delays. J Franklin Inst 349:1972–1988MathSciNetCrossRefMATH
17.
Monje CA, Chen YQ, Vinagre BM et al (2010) Fractional-order systems and controls. Springer, LondonCrossRefMATH
18.
Rakkiyappan R, Velmurugan G, Cao J (2015) Stability analysis of memristor-based fractional-order neural networks with different memductance functions. Cogn Neurodyn 9:145–177CrossRef
19.
Rihan FA, Lakshmanan S, Hashish AH et al (2015) Fractional-order delayed predator-Cprey systems with Holling type-II functional response. Nonlinear Dyn 80:777–789CrossRefMATH
20.
Podlubny I (1999) Fractional differential equations. Academic, New YorkMATH
21.
Song Q, Cao J (2006) Global exponential robust stability of Cohen–Grossberg neural network with time-varying delays and reaction-diffusion terms. J Franklin Inst 343:705–719MathSciNetCrossRefMATH
22.
Tian X, Xu R, Gan Q (2015) Hopf bifurcation analysis of a BAM neural network with multiple time delays and diffusion. Appl Math Comput 266:909–926MathSciNet
23.
Wang J, Wun H, Guo L (2013) Stability analysis of reaction-diffusion Cohen–Grossberg neural networks under impulsive control. Neurocomputing 106:21–30CrossRef
24.
Wang G, Xiao J, Wang Y et al (2014) Adaptive pinning cluster synchronization of fractional-order complex dynamical networks. Appl Math Comput 231:347–356MathSciNet
25.
Wang L, Xu D (2003) Global exponential stability of Hopfield reaction-diffusion neural networks with variable delays. Sci China Ser F 46:466–474MathSciNetCrossRefMATH
26.
Wang H, Yu Y, Wen G et al (2015) Stability analysis of fractional-order neural networks with time delay. Neural Process Lett 42:479–500CrossRef
27.
Wang L, Zou X (2002) Exponential stability of Cohen–Grossberg neural networks. Neural Netw 15:415–422CrossRef
28.
Wang Z, Zhang H (2010) Global asymptotic stability of reaction-diffusion Cohen–Grossberg neural networks with continuously distributed delays. IEEE Trans Neural Netw 21:39–49CrossRef
29.
Wu J (2001) Introduction to neural dynamics and signal transmission delay. Walter de Cruyter, BerlinCrossRefMATH
30.
Yang X, Song Q, Liu Y et al (2015) Finite-time stability analysis of fractional-order neural networks with delay. Neurocomputing 152:19–26CrossRef
31.
Zhao H, Wang K (2006) Dynamical behaviors of Cohen–Grossberg neural networks with delays and reaction-diffusion terms. Neurocomputing 70:536–543CrossRef
32.
Zheng P, Zhang J, Tang W (2010) Color image associative memory on a class of Cohen–Grossberg networks. Pattern Recogn 43:3255–3260CrossRefMATH
Metadaten
Titel
Stability and Hopf Bifurcation of Time Fractional Cohen–Grossberg Neural Networks with Diffusion and Time Delays in Leakage Terms
verfasst von
Xiaohong Tian
Rui Xu
Publikationsdatum
16.08.2016
Verlag
Springer US
Erschienen in
Neural Processing Letters / Ausgabe 2/2017
Print ISSN: 1370-4621
Elektronische ISSN: 1573-773X
DOI
https://doi.org/10.1007/s11063-016-9544-8

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