Stability and Bifurcation Analysis of a Three-Dimensional Recurrent Neural Network with Time Delay
We consider the nonlinear dynamical behavior of a three-dimensional recurrent neural network with time delay. By choosing the time delay as a bifurcation parameter, we prove that Hopf bifurcation occurs when the delay passes through a sequence of critical values. Applying the nor- mal form method an...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/357382 |
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| _version_ | 1832568195906535424 |
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| author | Yingguo Li |
| author_facet | Yingguo Li |
| author_sort | Yingguo Li |
| collection | DOAJ |
| description | We consider the nonlinear dynamical behavior of a
three-dimensional recurrent neural network with time delay. By choosing the
time delay as a bifurcation parameter, we prove that Hopf bifurcation occurs
when the delay passes through a sequence of critical values. Applying the nor-
mal form method and center manifold theory, we obtain some local bifurcation
results and derive formulas for determining the bifurcation direction and the
stability of the bifurcated periodic solution. Some numerical examples are also
presented to verify the theoretical analysis. |
| format | Article |
| id | doaj-art-0b3450f74b4a4c6494c4dea10764aeb3 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-0b3450f74b4a4c6494c4dea10764aeb32025-02-03T00:59:29ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/357382357382Stability and Bifurcation Analysis of a Three-Dimensional Recurrent Neural Network with Time DelayYingguo Li0School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, ChinaWe consider the nonlinear dynamical behavior of a three-dimensional recurrent neural network with time delay. By choosing the time delay as a bifurcation parameter, we prove that Hopf bifurcation occurs when the delay passes through a sequence of critical values. Applying the nor- mal form method and center manifold theory, we obtain some local bifurcation results and derive formulas for determining the bifurcation direction and the stability of the bifurcated periodic solution. Some numerical examples are also presented to verify the theoretical analysis.http://dx.doi.org/10.1155/2012/357382 |
| spellingShingle | Yingguo Li Stability and Bifurcation Analysis of a Three-Dimensional Recurrent Neural Network with Time Delay Journal of Applied Mathematics |
| title | Stability and Bifurcation Analysis of a Three-Dimensional Recurrent Neural Network with Time Delay |
| title_full | Stability and Bifurcation Analysis of a Three-Dimensional Recurrent Neural Network with Time Delay |
| title_fullStr | Stability and Bifurcation Analysis of a Three-Dimensional Recurrent Neural Network with Time Delay |
| title_full_unstemmed | Stability and Bifurcation Analysis of a Three-Dimensional Recurrent Neural Network with Time Delay |
| title_short | Stability and Bifurcation Analysis of a Three-Dimensional Recurrent Neural Network with Time Delay |
| title_sort | stability and bifurcation analysis of a three dimensional recurrent neural network with time delay |
| url | http://dx.doi.org/10.1155/2012/357382 |
| work_keys_str_mv | AT yingguoli stabilityandbifurcationanalysisofathreedimensionalrecurrentneuralnetworkwithtimedelay |