Stability and Bifurcation Analysis in a Class of Two-Neuron Networks with Resonant Bilinear Terms
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/697630 |
| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |