Bifurcation analysis on a discrete-time tabu learning model |
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Authors: | Min Xiao Jinde Cao |
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Institution: | aDepartment of Mathematics, Southeast University, Nanjing 210096, China;bDepartment of Mathematics, Nanjing Xiaozhuang College, Nanjing 210017, China |
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Abstract: | In this paper, we consider a discrete-time tabu learning single neuron model. After investigating the stability of the given system, we demonstrate that Pichfork bifurcation, Flip bifurcation and Neimark–Sacker bifurcation will occur when the bifurcation parameter exceed a critical value, respectively. A formula is given for determining the direction and stability of Neimark–Sacker bifurcation by applying the normal form theory and the center manifold theorem. Some numerical simulations for justifying the theoretical results are also provided. |
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Keywords: | Tabu learning Discrete-time Neural network Stability Pichfork/Flip/Neimark– Sacker bifurcation |
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