Stability and bifurcation analysis in trineuron model with time delay
 Xiaofeng Liao,
 Songtao Guo,
 Chuandong Li
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A simple delayed neural network model with three neurons is considered. By constructing suitable Lyapunov functions, we obtain sufficient delaydependent criteria to ensure global asymptotical stability of the equilibrium of a trineuron network with single time delay. Local stability of the model is investigated by analyzing the associated characteristic equation. It is found that Hopf bifurcation occurs when the time delay varies and passes a sequence of critical values. The stability and direction of bifurcating periodic solution are determined by applying the normal form theory and the center manifold theorem. If the associated characteristic equation of linearized system evaluated at a critical point involves a repeated pair of pure imaginary eigenvalues, then the double Hopf bifurcation is also found to occur in this model. Our main attention will be paid to the double Hopf bifurcation associated with resonance. Some Numerical examples are finally given for justifying the theoretical results.
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 Title
 Stability and bifurcation analysis in trineuron model with time delay
 Journal

Nonlinear Dynamics
Volume 49, Issue 12 , pp 319345
 Cover Date
 20070701
 DOI
 10.1007/s1107100691376
 Print ISSN
 0924090X
 Online ISSN
 1573269X
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Neural networks
 Time delay
 Global asymptotic stability
 Local stability
 Bifurcation
 Industry Sectors
 Authors

 Xiaofeng Liao ^{(1)} ^{(2)}
 Songtao Guo ^{(1)} ^{(2)}
 Chuandong Li ^{(1)} ^{(2)}
 Author Affiliations

 1. Department of Computer Science and Engineering, Chongqing University, Chongqing, 400030, P.R. China
 2. The Key Laboratory of Optoelectric Technology & Systems, Ministry of Education, Beijing, China