Global existence of periodic solutions in a simplified four-neuron BAM neural network model with multiple delays
<p>We consider a simplified bidirectional associated memory (BAM) neural network model with four neurons and multiple time delays. The global existence of periodic solutions bifurcating from Hopf bifurcations is investigated by applying the global Hopf bifurcation theorem due to Wu and Bendixs...
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| Format: | Article |
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| Language: | English |
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Wiley
2006-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://www.hindawi.com/GetArticle.aspx?doi=10.1155/DDNS/2006/57254 |
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| collection | DOAJ |
| description | <p>We consider a simplified bidirectional associated memory (BAM) neural network model with four neurons and multiple time delays. The global existence of periodic solutions bifurcating from Hopf bifurcations is investigated by applying the global Hopf bifurcation theorem due to Wu and Bendixson's criterion for high-dimensional ordinary differential equations due to Li and Muldowney. It is shown that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of the sum of two delays. Numerical simulations supporting the theoretical analysis are also included.</p> |
| format | Article |
| id | doaj-art-c0bbe60a622f456390c9ad91ba8316a0 |
| institution | Kabale University |
| issn | 1026-0226 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-c0bbe60a622f456390c9ad91ba8316a02025-02-03T05:48:05ZengWileyDiscrete Dynamics in Nature and Society1026-02262006-01-012006Global existence of periodic solutions in a simplified four-neuron BAM neural network model with multiple delays<p>We consider a simplified bidirectional associated memory (BAM) neural network model with four neurons and multiple time delays. The global existence of periodic solutions bifurcating from Hopf bifurcations is investigated by applying the global Hopf bifurcation theorem due to Wu and Bendixson's criterion for high-dimensional ordinary differential equations due to Li and Muldowney. It is shown that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of the sum of two delays. Numerical simulations supporting the theoretical analysis are also included.</p>http://www.hindawi.com/GetArticle.aspx?doi=10.1155/DDNS/2006/57254 |
| spellingShingle | Global existence of periodic solutions in a simplified four-neuron BAM neural network model with multiple delays Discrete Dynamics in Nature and Society |
| title | Global existence of periodic solutions in a simplified four-neuron BAM neural network model with multiple delays |
| title_full | Global existence of periodic solutions in a simplified four-neuron BAM neural network model with multiple delays |
| title_fullStr | Global existence of periodic solutions in a simplified four-neuron BAM neural network model with multiple delays |
| title_full_unstemmed | Global existence of periodic solutions in a simplified four-neuron BAM neural network model with multiple delays |
| title_short | Global existence of periodic solutions in a simplified four-neuron BAM neural network model with multiple delays |
| title_sort | global existence of periodic solutions in a simplified four neuron bam neural network model with multiple delays |
| url | http://www.hindawi.com/GetArticle.aspx?doi=10.1155/DDNS/2006/57254 |