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A coupling method of double memristors and analysis of extreme transient behavior

Abstract

By coupling a variable of the memristor in one memristive chaotic circuit with another memristor, an approach to construct a high-dimensional memristive chaotic system is proposed and a five-dimensional hidden chaotic system with double memristors is obtained. The Lyapunov fractal dimension and dynamics map of the system demonstrate that the system has extreme transient behaviors, such as chaos to period, chaos to quasi-period, quasi-period to another quasi-period, quasi-period to chaos, and chaos to another kind of chaos. The whole transition process experiences as many as 2, 3, 4, or even 5 different status. Besides, an interesting symmetric transient phenomenon is discovered and extreme multistability is also observed when changing the initial conditions. The extreme transient behavior is validated using the spectral entropy algorithm.

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Acknowledgements

This research was funded by the growth project of young scientific and technological talents in Guizhou for colleges and universities, Grant Number [KY [2020]142, KY [2019]160].

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Correspondence to Zhengping Zhang.

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Du, C., Liu, L., Zhang, Z. et al. A coupling method of double memristors and analysis of extreme transient behavior. Nonlinear Dyn 104, 765–787 (2021). https://doi.org/10.1007/s11071-021-06299-1

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Keywords

  • Memristive chaos
  • Coupled memristor system
  • Extreme transient transitions
  • Hidden attractor
  • Heterogeneous multistability