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Inventory Control Under Parametric Uncertainty of Underlying Models Read chapter Read first chapter

2013 | OriginalPaper | Chapter

Periodic Solution and Strange Attractor in Impulsive Hopfield Networks with Time-Varying Delays

Authors : Yanxia Cheng, Yan Yan, Zhanji Gui

Published in: IAENG Transactions on Engineering Technologies

Publisher: Springer Netherlands

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Abstract

By constructing suitable Lyapunov functions, we study the existence, uniqueness and global exponential stability of periodic solution for impulsive Hopfield neural networks with time-varying delays. Our condition extends and generalizes a known condition for the global exponential periodicity of continuous Hopfield neural networks with time-varying delays. Further the numerical simulation shows that our system can occur many forms of complexities including gui strange attractor and periodic solution.

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previous chapter Inventory Control Under Parametric Uncertainty of Underlying Models
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Literature
1.
Abou-El-Ela AMA, Sadekand AI, Mahmoud AM (2012) Existence and uniqueness of a periodic solution for third-order delay differential equation with two deviating arguments. IAENG Int J Appl Math, 42:1 \({\rm {IJAM}}\_42\_1\_02\)
2.
Akca H, Alassar R, Covachev V, Covacheva Z, Al-Zahrani E (2004) Continuoustime additive Hopfield-type neural networks with impulses. J Math Anal Appl 290(2):436–451MathSciNetMATHCrossRef
3.
Arika S, Tavsanoglu V (2005) Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays. Neurocomputing 68:161–176CrossRef
4.
Bainov DD, Simenov PS (1989) Systems with impulse effect: stability theory and applications. Ellis Horwood, ChichesterMATH
5.
Cao J, Jiang Q (2004) An analysis of periodic solutions of bi-directional associative memory networks with time-varying delays. Phys Lett A 330(3–4):203–213MathSciNetMATHCrossRef
6.
Cheng Y, Yan Y, Gui Z (2012) Existence and stability of periodic solution in impulsive Hopfield networks with time-varying delays. Lecture notes in engineering and computer science: Proceedings of the world congress on engineering WCE 2012, 4–6 July 2012 U.K , London, pp 18–23
7.
8.
Gui Z, Ge W (2006) Periodic solution and chaotic strange attractor for shunting inhibitory cellular neural networks with impulses. Chaos 16(3):1–10MathSciNetCrossRef
9.
Gui Z, Yang XS (2006) Stability and existence of periodic solutions of periodic cellular neural networks. Comput Math Appl 52(12):1657–1670MathSciNetMATHCrossRef
10.
Gui Z, Ge W (2007) Impulsive effect of continuous-time neural networks under pure structural variations. Int J Bifurcat Chaos 17(6):2127–2139MathSciNetMATHCrossRef
11.
Gui Z, Yang XS, Ge W (2007) Periodic solution for nonautonomous bidirectional associative memory neural networks with impulses. Neurocomputing 70(13–15):2517–2527CrossRef
12.
Lakshmikantham V, Baino DD, Simeonov P-S (1989) Theory of impulsive differential equations. World Scientific, SingaporeMATHCrossRef
13.
Li S, Liao X, Li C (2005) Hopf bifurcation of a two-neuron network with different discrete time delays. Int J Bifurcat Chaos 15(5):1589–1601MathSciNetMATHCrossRef
14.
Li Y (2005) Global exponential stability of BAM neural networks with delays and impulses. Chaos, Solitons Fractals 24(1):279–285MathSciNetMATH
15.
Li Y, Xing W, Lu L (2006) Existence and global exponential stability of periodic solution of a class of neural networks with impulses. Chaos, Solitons Fractals 27(2):437–445MathSciNetMATHCrossRef
16.
17.
Xu S, Lam J, Zou Y (2005) Delay-dependent approach to stabilization of time-delay chaotic systems via standard and delayed feedback controllers. Int J Bifurcat Chaos 15(4):1455–1465MathSciNetMATHCrossRef
18.
Yang X, Liao X, Evans DJ, Tang Y (2005) Existence and stability of periodic solution in impulsive Hopfield neural networks with finite distributed delays. Phys Lett A 343(1–3):108–116MATHCrossRef
Metadata
Title
Periodic Solution and Strange Attractor in Impulsive Hopfield Networks with Time-Varying Delays
Authors
Yanxia Cheng
Yan Yan
Zhanji Gui
Copyright Year
2013
Publisher
Springer Netherlands
Book
IAENG Transactions on Engineering Technologies

Print ISBN: 978-94-007-6189-6

Electronic ISBN: 978-94-007-6190-2

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-94-007-6190-2_2