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Nonlinear Dynamics

, Volume 96, Issue 3, pp 1879–1894 | Cite as

Hidden extreme multistability and dimensionality reduction analysis for an improved non-autonomous memristive FitzHugh–Nagumo circuit

  • Han BaoEmail author
  • Wenbo Liu
  • Mo Chen
Original Paper

Abstract

Due to the introduction of ideal memristors, extreme multistability has been found in many autonomous memristive circuits. However, such extreme multistability has not yet been reported in a non-autonomous memristive circuit. To this end, this paper presents an improved non-autonomous memristive FitzHugh–Nagumo circuit that possesses a smooth hyperbolic tangent memductance nonlinearity, from which coexisting infinitely many attractors are obtained. By utilizing voltage–current circuit model, a three-dimensional non-autonomous dynamical model is established, based on which the initial-dependent dynamics is explored by numerical plots and extreme multistability is thereby exhibited. To confirm that the improved non-autonomous memristive circuit operates in hidden oscillating patterns, an accurate two-dimensional non-autonomous dimensionality reduction model with initial-related parameters is further built by using incremental integral transformation, upon which stability analysis and bifurcation behaviors are elaborated. Because the equilibrium state of the dimensionality reduction model is always a stable node-focus, hidden extreme multistability with coexisting infinitely many attractors is truly confirmed. Finally, PSIM circuit simulations validate the initial-related hidden dynamical behaviors.

Keywords

FitzHugh–Nagumo circuit Ideal memristor Hidden extreme multistability Dimensionality reduction model 

Notes

Acknowledgements

This work was supported by the grants from the National Natural Science Foundations of China under 51777016, 61471191, and 61601062, and the Aeronautical Science Foundation of China under 20152052026.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflicts of interest.

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.College of Automation EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.School of Information Science and EngineeringChangzhou UniversityChangzhouChina

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