Stability and Hopf-Bifurcation Analysis of Delayed BAM Neural Network under Dynamic Thresholds
In this paper the dynamics of a three neuron model with self-connection and distributed delay under dynamical threshold is investigated. With the help of topological degree theory and Homotopy invariance principle existence and uniqueness of equilibrium point are established. The conditions for whic...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2009-10-01
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| Series: | Nonlinear Analysis |
| Subjects: | |
| Online Access: | http://www.journals.vu.lt/nonlinear-analysis/article/view/14466 |
| _version_ | 1819048676585111552 |
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| author | P. D. Gupta N. C. Majee A. B. Roy |
| author_facet | P. D. Gupta N. C. Majee A. B. Roy |
| author_sort | P. D. Gupta |
| collection | DOAJ |
| description | In this paper the dynamics of a three neuron model with self-connection and distributed delay under dynamical threshold is investigated. With the help of topological degree theory and Homotopy invariance principle existence and uniqueness of equilibrium point are established. The conditions for which the Hopf-bifurcation occurs at the equilibrium are obtained for the weak kernel of the distributed delay. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and central manifold theorem. Lastly global bifurcation aspect of such periodic solutions is studied. Some numerical simulations for justifying the theoretical analysis are also presented. |
| first_indexed | 2024-12-21T11:20:03Z |
| format | Article |
| id | doaj.art-bb5b3905fe76466f9f85c87f277cfd7d |
| institution | Directory Open Access Journal |
| issn | 1392-5113 2335-8963 |
| language | English |
| last_indexed | 2024-12-21T11:20:03Z |
| publishDate | 2009-10-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj.art-bb5b3905fe76466f9f85c87f277cfd7d2022-12-21T19:05:49ZengVilnius University PressNonlinear Analysis1392-51132335-89632009-10-0114410.15388/NA.2009.14.4.14466Stability and Hopf-Bifurcation Analysis of Delayed BAM Neural Network under Dynamic ThresholdsP. D. Gupta0N. C. Majee1A. B. Roy2Jadavpur University, IndiaJadavpur University, IndiaJadavpur University, IndiaIn this paper the dynamics of a three neuron model with self-connection and distributed delay under dynamical threshold is investigated. With the help of topological degree theory and Homotopy invariance principle existence and uniqueness of equilibrium point are established. The conditions for which the Hopf-bifurcation occurs at the equilibrium are obtained for the weak kernel of the distributed delay. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and central manifold theorem. Lastly global bifurcation aspect of such periodic solutions is studied. Some numerical simulations for justifying the theoretical analysis are also presented.http://www.journals.vu.lt/nonlinear-analysis/article/view/14466BAM neural networkdistributed delayHopf-bifurcationstability and direction of Hopf-bifurcationglobal Hopf-bifurcation |
| spellingShingle | P. D. Gupta N. C. Majee A. B. Roy Stability and Hopf-Bifurcation Analysis of Delayed BAM Neural Network under Dynamic Thresholds Nonlinear Analysis BAM neural network distributed delay Hopf-bifurcation stability and direction of Hopf-bifurcation global Hopf-bifurcation |
| title | Stability and Hopf-Bifurcation Analysis of Delayed BAM Neural Network under Dynamic Thresholds |
| title_full | Stability and Hopf-Bifurcation Analysis of Delayed BAM Neural Network under Dynamic Thresholds |
| title_fullStr | Stability and Hopf-Bifurcation Analysis of Delayed BAM Neural Network under Dynamic Thresholds |
| title_full_unstemmed | Stability and Hopf-Bifurcation Analysis of Delayed BAM Neural Network under Dynamic Thresholds |
| title_short | Stability and Hopf-Bifurcation Analysis of Delayed BAM Neural Network under Dynamic Thresholds |
| title_sort | stability and hopf bifurcation analysis of delayed bam neural network under dynamic thresholds |
| topic | BAM neural network distributed delay Hopf-bifurcation stability and direction of Hopf-bifurcation global Hopf-bifurcation |
| url | http://www.journals.vu.lt/nonlinear-analysis/article/view/14466 |
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