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Stability and bifurcation analysis for a neural network model with discrete and distributed delays
Author(s) -
Du Yanke,
Xu Rui,
Liu Qiming
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2568
Subject(s) - mathematics , bifurcation , hopf bifurcation , saddle node bifurcation , biological applications of bifurcation theory , stability (learning theory) , chaotic , bifurcation diagram , period doubling bifurcation , transcritical bifurcation , mathematical analysis , control theory (sociology) , nonlinear system , computer science , physics , control (management) , quantum mechanics , machine learning , artificial intelligence
In this paper, a two‐neuron network with both discrete and distributed delays is considered. With the corresponding characteristic equation analyzed, the local stability of the trivial equilibrium is investigated. With the discrete time delay taken as a bifurcation parameter, the existence of Hopf bifurcation is established. Moreover, formulae for determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are derived. Finally, numerical simulations are carried out to illustrate the main results and further to exhibit that there is a characteristic sequence of bifurcations leading to a chaotic dynamics, which implies that the system admits rich and complex dynamics. Copyright © 2012 John Wiley & Sons, Ltd.