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On hyperchaos in a small memristive neural network

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Abstract

This paper studies a small Hopfield neural network with a memristive synaptic weight. We show that the previous stable network after one weight replaced by a memristor can exhibit rich complex dynamics, such as quasi-periodic orbits, chaos, and hyperchaos, which suggests that the memristor is crucial to the behaviors of neural networks and may play a significant role. We also prove the existence of a saddle periodic orbit, and then present computer-assisted verification of hyperchaos through a homoclinic intersection of the stable and unstable manifolds, which gives a positive answer to an interesting question that whether a 4D memristive system with a line of equilibria can demonstrate hyperchaos.

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Notes

  1. A C++ package for rigorous computation of dynamical systems by CAPD Group, website http://capd.wsb-nlu.edu.pl.

  2. GNU Multiple Precision Arithmetic Library, website http://gmplib.org.

  3. A C library for multiple-precision floating-point computations with correct rounding, website http://www.mpfr.org.

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Acknowledgments

We are very grateful to the reviewers for their valuable comments and suggestions. This work is supported in part by the National Natural Science Foundation of China (61104150), Science Fund for Distinguished Young Scholars of Chongqing (cstc2013jcyjjq40001), and the Science and Technology Project of Chongqing Education Commission (KJ130517).

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Authors and Affiliations

  1. Key Laboratory of Industrial Internet of Things & Networked Control of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing,  400065, China

    Qingdu Li, Song Tang & Tingting Zhou

  2. Research Center of Analysis and Control for Complex Systems, Chongqing University of Posts and Telecommunications, Chongqing,  400065, China

    Hongzheng Zeng

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  1. Qingdu Li
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  2. Song Tang
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  3. Hongzheng Zeng
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  4. Tingting Zhou
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Correspondence to Qingdu Li.

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Li, Q., Tang, S., Zeng, H. et al. On hyperchaos in a small memristive neural network. Nonlinear Dyn 78, 1087–1099 (2014). https://doi.org/10.1007/s11071-014-1498-7

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  • DOI: https://doi.org/10.1007/s11071-014-1498-7

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