Stability and Bifurcation Analysis for a Class of Generalized Reaction-Diffusion Neural Networks with Time Delay
Considering the fact that results for static neural networks are much more scare than results for local field neural networks and our purpose letting the problem researched be more general in many aspects, in this paper, a generalized neural networks model which includes reaction-diffusion local fie...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/4321358 |
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| _version_ | 1849400383345000448 |
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| author | Tianshi Lv Qintao Gan Qikai Zhu |
| author_facet | Tianshi Lv Qintao Gan Qikai Zhu |
| author_sort | Tianshi Lv |
| collection | DOAJ |
| description | Considering the fact that results for static neural networks are much more scare than results for local field neural networks and our purpose letting the problem researched be more general in many aspects, in this paper, a generalized neural networks model which includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks is built and the stability and bifurcation problems for it are investigated under Neumann boundary conditions. First, by discussing the corresponding characteristic equations, the local stability of the trivial uniform steady state is discussed and the existence of Hopf bifurcations is shown. By using the normal form theory and the center manifold reduction of partial function differential equations, explicit formulae which determine the direction and stability of bifurcating periodic solutions are acquired. Finally, numerical simulations show the results. |
| format | Article |
| id | doaj-art-88ebbead9aee4cd59991fa3f88d586e1 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-88ebbead9aee4cd59991fa3f88d586e12025-08-20T03:38:05ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/43213584321358Stability and Bifurcation Analysis for a Class of Generalized Reaction-Diffusion Neural Networks with Time DelayTianshi Lv0Qintao Gan1Qikai Zhu2Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaInstitute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaInstitute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaConsidering the fact that results for static neural networks are much more scare than results for local field neural networks and our purpose letting the problem researched be more general in many aspects, in this paper, a generalized neural networks model which includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks is built and the stability and bifurcation problems for it are investigated under Neumann boundary conditions. First, by discussing the corresponding characteristic equations, the local stability of the trivial uniform steady state is discussed and the existence of Hopf bifurcations is shown. By using the normal form theory and the center manifold reduction of partial function differential equations, explicit formulae which determine the direction and stability of bifurcating periodic solutions are acquired. Finally, numerical simulations show the results.http://dx.doi.org/10.1155/2016/4321358 |
| spellingShingle | Tianshi Lv Qintao Gan Qikai Zhu Stability and Bifurcation Analysis for a Class of Generalized Reaction-Diffusion Neural Networks with Time Delay Discrete Dynamics in Nature and Society |
| title | Stability and Bifurcation Analysis for a Class of Generalized Reaction-Diffusion Neural Networks with Time Delay |
| title_full | Stability and Bifurcation Analysis for a Class of Generalized Reaction-Diffusion Neural Networks with Time Delay |
| title_fullStr | Stability and Bifurcation Analysis for a Class of Generalized Reaction-Diffusion Neural Networks with Time Delay |
| title_full_unstemmed | Stability and Bifurcation Analysis for a Class of Generalized Reaction-Diffusion Neural Networks with Time Delay |
| title_short | Stability and Bifurcation Analysis for a Class of Generalized Reaction-Diffusion Neural Networks with Time Delay |
| title_sort | stability and bifurcation analysis for a class of generalized reaction diffusion neural networks with time delay |
| url | http://dx.doi.org/10.1155/2016/4321358 |
| work_keys_str_mv | AT tianshilv stabilityandbifurcationanalysisforaclassofgeneralizedreactiondiffusionneuralnetworkswithtimedelay AT qintaogan stabilityandbifurcationanalysisforaclassofgeneralizedreactiondiffusionneuralnetworkswithtimedelay AT qikaizhu stabilityandbifurcationanalysisforaclassofgeneralizedreactiondiffusionneuralnetworkswithtimedelay |