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Two-memristor-based Chua’s hyperchaotic circuit with plane equilibrium and its extreme multistability

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Abstract

This paper presents a novel fifth-order two-memristor-based Chua’s hyperchaotic circuit, which is synthesized from an active band pass filter-based Chua’s circuit through replacing a nonlinear resistor and a linear resistor with two different memristors. This physical circuit has a plane equilibrium and therefore emerges complex phenomenon of extreme multistability. Based on the mathematical model, stability distributions of three nonzero eigenvalues in the equilibrium plane are exhibited, from which it is observed that four different stability regions with unstable saddle-focus, and stable and unstable node-focus are distributed, thereby leading to coexisting phenomenon of infinitely many attractors. Furthermore, extreme multistability depending on two-memristor initial conditions is investigated by bifurcation diagrams and Lyapunov exponent spectra and coexisting infinitely many attractors’ behavior is revealed by phase portraits and attraction basins. At last, a hardware circuit is fabricated and some experimental observations are captured to verify that extreme multistability indeed exists in the two-memristor-based Chua’s hyperchaotic circuit.

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Acknowledgements

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

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Correspondence to Bocheng Bao.

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Bao, B., Jiang, T., Wang, G. et al. Two-memristor-based Chua’s hyperchaotic circuit with plane equilibrium and its extreme multistability. Nonlinear Dyn 89, 1157–1171 (2017) doi:10.1007/s11071-017-3507-0

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Keywords

  • Memristive circuit
  • Plane equilibrium
  • Infinitely many attractor
  • Extreme multistability