Stability and bifurcation analysis for a neural network model with discrete and distributed delays. (5th June 2012)

• Record Type: Journal Article
• Authors: Du, Yanke; Xu, Rui; Liu, Qiming
• Is Part Of: Mathematical methods in the applied sciences. Volume 36:Number 1(2013:Jan. 15)
• Page Start: 49
• Page End: 59
• Publication Date: 2012-06-05
• Subjects: Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.2568
• Languages: English
• ISSNs: 0170-4214

Abstract

<abstract abstract-type="main" id="mma2568-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p id="mma2568-para-0001">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 &amp; Sons, Ltd.</p> </abstract>