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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| Format: | Article |
| Language: | English |
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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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| author | Changjin Xu |
| author_facet | Changjin Xu |
| author_sort | Changjin Xu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e9ce20fd23644ccab7112e146bb2b503 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e9ce20fd23644ccab7112e146bb2b5032025-02-03T01:12:30ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/546356546356Neimark-Sacker Bifurcation Analysis for a Discrete-Time System of Two NeuronsChangjin Xu0Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550004, ChinaA 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.http://dx.doi.org/10.1155/2012/546356 |
| spellingShingle | Changjin Xu Neimark-Sacker Bifurcation Analysis for a Discrete-Time System of Two Neurons Abstract and Applied Analysis |
| title | Neimark-Sacker Bifurcation Analysis for a Discrete-Time System of Two Neurons |
| title_full | Neimark-Sacker Bifurcation Analysis for a Discrete-Time System of Two Neurons |
| title_fullStr | Neimark-Sacker Bifurcation Analysis for a Discrete-Time System of Two Neurons |
| title_full_unstemmed | Neimark-Sacker Bifurcation Analysis for a Discrete-Time System of Two Neurons |
| title_short | Neimark-Sacker Bifurcation Analysis for a Discrete-Time System of Two Neurons |
| title_sort | neimark sacker bifurcation analysis for a discrete time system of two neurons |
| url | http://dx.doi.org/10.1155/2012/546356 |
| work_keys_str_mv | AT changjinxu neimarksackerbifurcationanalysisforadiscretetimesystemoftwoneurons |