Stability and Hopf Bifurcation of an n-Neuron Cohen-Grossberg Neural Network with Time Delays
A Cohen-Grossberg neural network with discrete delays is investigated in this paper. Sufficient conditions for the existence of local Hopf bifurcation are obtained by analyzing the distribution of roots of characteristic equation. Moreover, the direction and stability of Hopf bifurcation are obtaine...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/468584 |
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| _version_ | 1832555840052133888 |
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| author | Qiming Liu Sumin Yang |
| author_facet | Qiming Liu Sumin Yang |
| author_sort | Qiming Liu |
| collection | DOAJ |
| description | A Cohen-Grossberg neural network with discrete delays is investigated in this paper. Sufficient conditions for the existence of local Hopf bifurcation are obtained by analyzing the distribution of roots of characteristic equation. Moreover, the direction and stability of Hopf bifurcation are obtained by applying the normal form theory and the center manifold theorem. Numerical simulations are given to illustrate the obtained results. |
| format | Article |
| id | doaj-art-08e0a4967e2e4232b53e3eaadd2999d3 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-08e0a4967e2e4232b53e3eaadd2999d32025-02-03T05:46:59ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/468584468584Stability and Hopf Bifurcation of an n-Neuron Cohen-Grossberg Neural Network with Time DelaysQiming Liu0Sumin Yang1Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaDepartment of Information Engineering, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaA Cohen-Grossberg neural network with discrete delays is investigated in this paper. Sufficient conditions for the existence of local Hopf bifurcation are obtained by analyzing the distribution of roots of characteristic equation. Moreover, the direction and stability of Hopf bifurcation are obtained by applying the normal form theory and the center manifold theorem. Numerical simulations are given to illustrate the obtained results.http://dx.doi.org/10.1155/2014/468584 |
| spellingShingle | Qiming Liu Sumin Yang Stability and Hopf Bifurcation of an n-Neuron Cohen-Grossberg Neural Network with Time Delays Journal of Applied Mathematics |
| title | Stability and Hopf Bifurcation of an n-Neuron Cohen-Grossberg Neural Network with Time Delays |
| title_full | Stability and Hopf Bifurcation of an n-Neuron Cohen-Grossberg Neural Network with Time Delays |
| title_fullStr | Stability and Hopf Bifurcation of an n-Neuron Cohen-Grossberg Neural Network with Time Delays |
| title_full_unstemmed | Stability and Hopf Bifurcation of an n-Neuron Cohen-Grossberg Neural Network with Time Delays |
| title_short | Stability and Hopf Bifurcation of an n-Neuron Cohen-Grossberg Neural Network with Time Delays |
| title_sort | stability and hopf bifurcation of an n neuron cohen grossberg neural network with time delays |
| url | http://dx.doi.org/10.1155/2014/468584 |
| work_keys_str_mv | AT qimingliu stabilityandhopfbifurcationofannneuroncohengrossbergneuralnetworkwithtimedelays AT suminyang stabilityandhopfbifurcationofannneuroncohengrossbergneuralnetworkwithtimedelays |