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Memristor synapse-coupled memristive neuron network: synchronization transition and occurrence of chimera

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Abstract

Memristor synapse can be used to characterize the electromagnetic induction effect between two neurons that induces an action current by their membrane potential difference. This paper proposes a memristor synapse-coupled neuron network with no equilibrium, which is achieved using a memristor synapse to connect the membrane potentials of two identical three-dimensional memristive Hindmarsh–Rose neurons. Exponential synchronization is proved theoretically, and synchronous activities are discussed numerically. The theoretical and numerical results illustrate that the synchronicities of memristor synapse-coupled neuron network are related to the memristor coupling coefficient and especially related to the initial states of memristor synapse and coupling neurons. Furthermore, by constructing a ring network of memristor synapse-coupled neuron network, several types of collective behaviors including incoherent, coherent, imperfect synchronization, and chimera states are disclosed numerically, which indicate that the chimera states arisen in the ring network are dependent on the memristor coupling coefficient and sub-network coupling strength.

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Acknowledgements

This work was supported by the grants from the National Key Research and Development Program of China under 2018YFB2003304 and the National Natural Science Foundations of China under 51777016 and 61801054, the Postgraduate Research & Practice Innovation Program of Jiangsu Province, China under KYCX19_0172, and the Doctoral Students’ Short Term Study Abroad Fund of Nanjing University of Aeronautics and Astronautics, China under 190601DF02.

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Authors and Affiliations

  1. College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China

    Han Bao & Wenbo Liu

  2. School of Information Engineering, Xuchang University, Xuchang, 461000, China

    Yunzhen Zhang

  3. School of Information Science and Engineering, Changzhou University, Changzhou, 213164, China

    Bocheng Bao

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  1. Han Bao
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Bao, H., Zhang, Y., Liu, W. et al. Memristor synapse-coupled memristive neuron network: synchronization transition and occurrence of chimera. Nonlinear Dyn 100, 937–950 (2020). https://doi.org/10.1007/s11071-020-05529-2

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