Dynamical analysis of a delayed six‐neuron BAM network |
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| Authors: | Chengdai Huang Ning Li Jinde Cao Tasawar Hayat |
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| Affiliation: | 1. Department of Mathematics, Southeast University, Nanjing, China;2. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia;3. Department of Mathematics, Quaid–I–Azam University, Islamabad, Pakistan |
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| Abstract: | In this article, a simplified bidirectional associative memory network with delays involving six neurons is considered. By analyzing the distribution of roots of the characteristic equation for linearized system regarding the sum of delay as a bifurcation parameter, we obtain the condition of the occurrence for Hopf bifurcation. It reveals that Hopf bifurcation occurs when the sum of the delay passes through a critical value. The direction and the stability of the bifurcating periodic solution are determined by applying the normal form theory and center manifold theorem. Finally, a numerical example is used to illustrate the validity of theoretical results obtained. © 2015 Wiley Periodicals, Inc. Complexity 21: 9–28, 2016 |
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| Keywords: | bidirectional associative memory network stability Hopf bifurcation time delay periodic solution |
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