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Coexisting firing patterns and phase synchronization in locally active memristor coupled neurons with HR and FN models

Abstract

Local activity is regarded as the origin of complexity. In this study, a locally active memristor with coexisting two stable pinched hysteresis loops and two local activity regions is proposed. Its nonvolatile memory, as well as locally active characteristics, is validated by the power-off plot and DC VI plot. Based on two-dimensional Hindmarsh–Rose and two-dimensional Fitzhugh–Nagumo neurons, a simple neural network is constructed by connecting the two neurons with the locally active memristor. Coexisting multiple firing patterns under different initial conditions are investigated by considering the coupling strength as a unique controlled parameter. The results suggest that the system exhibits coexisting periodic and chaotic bursting firing patterns as well as coexisting two periodic firing patterns with different topologies. Furthermore, state switching without parameters is also explored. In particular, phase synchronization of the memristor synapse-coupled neurons is discussed, which implies that two nonidentical neurons gradually become phase synchronized with the increase in the coupling strength. In order to confirm the effectiveness of numerical simulations, circuit simulations are included.

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Acknowledgements

This work was supported by the National Key Research and Development Program of China (Grant No. 2018AAA0103300).

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Correspondence to Zhijun Li.

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Li, Z., Zhou, H., Wang, M. et al. Coexisting firing patterns and phase synchronization in locally active memristor coupled neurons with HR and FN models. Nonlinear Dyn 104, 1455–1473 (2021). https://doi.org/10.1007/s11071-021-06315-4

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Keywords

  • Locally active memristor
  • Coupling strength
  • Coexisting multiple firing patterns
  • Phase synchronization