Dynamics and control in an $$({\varvec{n}}+{\varvec{2}})$$ ( n + 2 ) -neuron BAM network with multiple delays
| Autor: | Ahmed M. Elaiw, Jinde Cao, Abdullah AI-Mazrooei, Abdulaziz Alofi, Chengdai Huang |
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| Rok vydání: | 2016 |
| Předmět: |
Hopf bifurcation
Distribution (number theory) Applied Mathematics Mechanical Engineering Mathematical analysis Characteristic equation Aerospace Engineering Ocean Engineering Saddle-node bifurcation 02 engineering and technology Bifurcation diagram 01 natural sciences Stability (probability) symbols.namesake Control and Systems Engineering 0103 physical sciences 0202 electrical engineering electronic engineering information engineering symbols Applied mathematics 020201 artificial intelligence & image processing Electrical and Electronic Engineering 010301 acoustics Center manifold Bifurcation Mathematics |
| Zdroj: | Nonlinear Dynamics. 87:313-336 |
| ISSN: | 1573-269X 0924-090X |
| Popis: | The issues of the stability and bifurcation for a delayed BAM network involving two neurons in the I-layer and arbitrary neurons in the J-layer are concerned in the present paper. By adopting the sum of the delays as the bifurcation parameter, we discuss the distribution of the roots of the characteristic equation for high-dimension system in terms of stability switches theory and further present some sufficient conditions for the occurrence of Hopf bifurcations. Analysis reveals that Hopf bifurcation will emerge after the given system loses its stability. Moreover, we derive explicit general formulae to determine the properties of bifurcation via the normal theory and the center manifold theorem. It is demonstrated that the sum of the delays can effectively affect the dynamics of the proposed system. Finally, an illustrative example is employed to verify the validity of the theoretical results obtained. |
| Databáze: | OpenAIRE |
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