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- Title
Stability and Hopf bifurcation in a three-neuron unidirectional ring with distributed delays.
- Authors
Han, Yanyan; Song, Yongli
- Abstract
In this paper, we consider the effect of distributed delays in a three-neuron unidirectional ring. Sufficient conditions for existence of unique equilibrium, multiple equilibria and their local stability are derived. Taking the average delay as a bifurcation parameter, we find two critical values at which the system undergoes Hopf bifurcations. The orbital asymptotic stability of the Hopf bifurcating periodic solutions is investigated by using the method of multiple scales. The global Hopf bifurcation is also studied. Finally, the theoretical results are illustrated by some numerical simulations.
- Subjects
ARTIFICIAL neural networks; STABILITY (Mechanics); HOPF bifurcations; EQUILIBRIUM; COMPUTER simulation
- Publication
Nonlinear Dynamics, 2012, Vol 69, Issue 1/2, p357
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-011-0269-y