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Fold-flip bifurcation analysis on a class of discrete-time neural network

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Abstract

This paper reports fold-flip bifurcation on a class of discrete-time neural network. Sufficient conditions are given to demonstrate fold-flip bifurcation. By performing linear and nonlinear transformation, the normal form and versal unfolding are derived to obtain the bifurcation diagrams of the truncated normal form such as fold bifurcation, flip bifurcation, and the Neimark–Sacker bifurcation of the period-2 cycle. Some numerical simulations are given to support the analytic results.

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Acknowledgments

This research is supported by the National Natural Science Foundation of China Grant No. 60974020 and the Fundamental Research Funds for the Central Universities of China (Project No. CDJZR10 18 55 01).

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Authors and Affiliations

  1. College of Computer Science, Chongqing University, Chongqing, 400030, People’s Republic of China

    Xing He & Chuandong Li

  2. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, People’s Republic of China

    Yonglu Shu

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  1. Xing He
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  2. Chuandong Li
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  3. Yonglu Shu
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Correspondence to Chuandong Li.

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He, X., Li, C. & Shu, Y. Fold-flip bifurcation analysis on a class of discrete-time neural network. Neural Comput & Applic 22, 375–381 (2013). https://doi.org/10.1007/s00521-011-0699-y

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  • DOI: https://doi.org/10.1007/s00521-011-0699-y

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