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Bifurcation analysis on a two-neuron system with distributed delays
A general two-neuron model with distributed delays is studied in this paper. Its local linear stability is analyzed by using the Routh–Hurwitz criterion. If the mean delay is used as a bifurcation parameter, we prove that Hopf bifurcation occurs for a weak kernel. This means that a family of periodi...
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Published in: | Physica. D 2001-02, Vol.149 (1), p.123-141 |
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container_title | Physica. D |
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creator | Liao, Xiaofeng Wong, Kwok-Wo Wu, Zhongfu |
description | A general two-neuron model with distributed delays is studied in this paper. Its local linear stability is analyzed by using the Routh–Hurwitz criterion. If the mean delay is used as a bifurcation parameter, we prove that Hopf bifurcation occurs for a weak kernel. This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem. Some numerical simulations for justifying the theoretical analysis are also given. |
doi_str_mv | 10.1016/S0167-2789(00)00197-4 |
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Its local linear stability is analyzed by using the Routh–Hurwitz criterion. If the mean delay is used as a bifurcation parameter, we prove that Hopf bifurcation occurs for a weak kernel. This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem. Some numerical simulations for justifying the theoretical analysis are also given.</description><subject>Distributed delay</subject><subject>Hopf bifurcation</subject><subject>Neural network</subject><subject>Periodic solutions</subject><issn>0167-2789</issn><issn>1872-8022</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2001</creationdate><recordtype>article</recordtype><recordid>eNqFkM1LxDAQxYMouK7-CUJPoodqPrpNexJd_IIFD-o5pMkEI912zaQu_e83uytevcy8gfcezI-Qc0avGWXlzVsaMueyqi8pvaKU1TIvDsiEVZLnFeX8kEz-LMfkBPGLJpcUckLm994Nwejo-y7TnW5H9JhtdRbXfd7BENKBI0ZYZmsfPzPrMQbfDBFsZqHVI56SI6dbhLPfPSUfjw_v8-d88fr0Mr9b5EaIKuaGWcfrShSs4RqcFYw1VlKomdHO1sJVrqw147Yu2GzGHeiK87JIqnG8ACmm5GLfuwr99wAY1dKjgbbVHfQDKl6WqZyJZJztjSb0iAGcWgW_1GFUjKotMrVDprY8FKVqh0wVKXe7z0H64sdDUGg8dAasD2Cisr3_p2EDU9Zz-g</recordid><startdate>20010201</startdate><enddate>20010201</enddate><creator>Liao, Xiaofeng</creator><creator>Wong, Kwok-Wo</creator><creator>Wu, Zhongfu</creator><general>Elsevier B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20010201</creationdate><title>Bifurcation analysis on a two-neuron system with distributed delays</title><author>Liao, Xiaofeng ; Wong, Kwok-Wo ; Wu, Zhongfu</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c338t-c1df298341b2aefd311bd70e91cafd93f8f69a12d941552fea8226452fbf24e73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2001</creationdate><topic>Distributed delay</topic><topic>Hopf bifurcation</topic><topic>Neural network</topic><topic>Periodic solutions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liao, Xiaofeng</creatorcontrib><creatorcontrib>Wong, Kwok-Wo</creatorcontrib><creatorcontrib>Wu, Zhongfu</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Physica. D</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liao, Xiaofeng</au><au>Wong, Kwok-Wo</au><au>Wu, Zhongfu</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Bifurcation analysis on a two-neuron system with distributed delays</atitle><jtitle>Physica. D</jtitle><date>2001-02-01</date><risdate>2001</risdate><volume>149</volume><issue>1</issue><spage>123</spage><epage>141</epage><pages>123-141</pages><issn>0167-2789</issn><eissn>1872-8022</eissn><abstract>A general two-neuron model with distributed delays is studied in this paper. Its local linear stability is analyzed by using the Routh–Hurwitz criterion. If the mean delay is used as a bifurcation parameter, we prove that Hopf bifurcation occurs for a weak kernel. This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value. 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subjects | Distributed delay Hopf bifurcation Neural network Periodic solutions |
title | Bifurcation analysis on a two-neuron system with distributed delays |
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