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Controlling extreme multistability of memristor emulator-based dynamical circuit in flux–charge domain

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Abstract

Memristive circuit with infinitely many equilibrium points can exhibit the special phenomenon of extreme multistability, whose dynamics mechanism and physical control are significant issues deserving in-depth investigations. In this paper, a control strategy for extreme multistability exhibited in an active band pass filter-based memristive circuit is explored in flux–charge domain. To this end, an incremental flux–charge model is established with four additional constant parameters reflecting the initial conditions of all dynamic elements. Thus, the line equilibrium point only related to memristor initial condition in the voltage–current domain is transformed into some determined equilibrium points, whose locations and stabilities are explicitly related to all four initial conditions. Consequently, the initial condition-dependent extreme multistability phenomenon, which has not been quantitatively analyzed in the voltage–current domain, can readily be investigated through evaluating these determined equilibrium points. Most important of all, the initial condition-dependent dynamical behaviors are formulated as the system parameter-dependent behaviors in the newly constructed flux–charge model and thus can be rigorously captured in a hardware equivalent realization circuit. Numerical simulations and experimental measurements reveal that the control of extreme multistability is successfully achieved in flux–charge domain, which is significant for seeking potential engineering applications of multistable memristive circuits.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant Nos. 61601062, 51607013, and 51277017 and the Natural Science Foundation of Jiangsu Province, China, under Grant No. BK20160282.

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Correspondence to Bocheng Bao.

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Chen, M., Sun, M., Bao, B. et al. Controlling extreme multistability of memristor emulator-based dynamical circuit in flux–charge domain. Nonlinear Dyn 91, 1395–1412 (2018). https://doi.org/10.1007/s11071-017-3952-9

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Keywords

  • Flux–charge domain
  • Memristive circuit
  • Extreme multistability
  • Equilibrium point
  • Control