Neimark-Sacker Bifurcation Analysis for a Discrete-Time System of Two Neurons
A class of discrete-time system modelling a network with two neurons is considered. First, we investigate the global stability of the given system. Next, we study the local stability by techniques developed by Kuznetsov to discrete-time systems. It is found that Neimark-Sacker bifurcation (or Hopf b...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/546356 |
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| Summary: | A class of discrete-time system modelling a network with two neurons is considered. First, we investigate the global stability of the given system. Next, we study the local stability by techniques developed by Kuznetsov to discrete-time systems. It is found that Neimark-Sacker bifurcation (or Hopf bifurcation for map) will occur when the bifurcation parameter exceeds a critical value. A formula determining the direction and stability of Neimark-Sacker bifurcation by applying normal form theory and center manifold theorem is given. Finally, some numerical simulations for justifying the theoretical results are also provided. |
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| ISSN: | 1085-3375 1687-0409 |