In:
Abstract and Applied Analysis, Hindawi Limited, Vol. 2011 ( 2011), p. 1-21
Abstract:
A class of two-neuron networks with resonant bilinear terms is considered. The stability of the zero equilibrium and existence of Hopf bifurcation is studied. It is shown that the zero equilibrium is locally asymptotically stable when the time delay is small enough, while change of stability of the zero equilibrium will cause a bifurcating periodic solution as the time delay passes through a sequence of critical values. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Finally, numerical simulations supporting the theoretical analysis are carried out.
Type of Medium:
Online Resource
ISSN:
1085-3375
,
1687-0409
Language:
English
Publisher:
Hindawi Limited
Publication Date:
2011
detail.hit.zdb_id:
2064801-7
SSG:
17,1
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