This paper reveals the dynamical behaviors of a bidirectional neural network consisting of four neurons with delayed nearest-neighbor and shortcut connections. The criterion of the global asymptotic stability of the trivial equilibrium of the network is derived by means of a suitable Lyapunov functional. The local stability of the trivial equilibrium is investigated by analyzing the distributions of roots of the associated characteristic equation. The sufficient conditions for the existence of nontrivial synchronous and asynchronous equilibria and periodic oscillations arising from codimension one bifurcations are obtained. Multistability near the codimension two bifurcation points is presented. Numerical simulations are given to validate the theoretical analysis.
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October 2010
Research Papers
Stability and Bifurcation Analysis of a Network of Four Neurons With Time Delays
Xiaochen Mao,
Xiaochen Mao
MOE Key Laboratory of Mechanics and Control for Aerospace Structures,
Nanjing University of Aeronautics and Astronautics
, 210016 Nanjing, China; Department of Engineering Mechanics, College of Mechanics and Materials, Hohai University
, 210098 Nanjing, China
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Haiyan Hu
Haiyan Hu
MOE Key Laboratory of Mechanics and Control for Aerospace Structures,
Nanjing University of Aeronautics and Astronautics
, 210016 Nanjing, China
Search for other works by this author on:
Xiaochen Mao
MOE Key Laboratory of Mechanics and Control for Aerospace Structures,
Nanjing University of Aeronautics and Astronautics
, 210016 Nanjing, China; Department of Engineering Mechanics, College of Mechanics and Materials, Hohai University
, 210098 Nanjing, China
Haiyan Hu
MOE Key Laboratory of Mechanics and Control for Aerospace Structures,
Nanjing University of Aeronautics and Astronautics
, 210016 Nanjing, ChinaJ. Comput. Nonlinear Dynam. Oct 2010, 5(4): 041001 (6 pages)
Published Online: June 29, 2010
Article history
Received:
September 19, 2008
Revised:
April 22, 2009
Online:
June 29, 2010
Published:
June 29, 2010
Citation
Mao, X., and Hu, H. (June 29, 2010). "Stability and Bifurcation Analysis of a Network of Four Neurons With Time Delays." ASME. J. Comput. Nonlinear Dynam. October 2010; 5(4): 041001. https://doi.org/10.1115/1.4000317
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