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Antimonotonicity, chaos and multiple attractors in a novel autonomous memristor-based jerk circuit

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Abstract

A novel memristor-based oscillator derived from the autonomous jerk circuit (Sprott in IEEE Trans Circuits Syst II Express Briefs 58:240–243, 2011) is proposed. A first-order memristive diode bridge replaces the semiconductor diode of the original circuit. The complex behavior of the oscillator is investigated in terms of equilibria and stability, phase space trajectories plots, bifurcation diagrams, graphs of Lyapunov exponents, as well as frequency spectra. Antimonotonicity (i.e. concurrent creation and destruction of periodic orbits), chaos, periodic windows and crises are reported. More interestingly, one of the main features of the novel memristive jerk circuit is the presence of a region in the parameters’ space in which the model develops hysteretic behavior. This later phenomenon is marked by the coexistence of four different (periodic and chaotic) attractors for the same values of system parameters, depending solely on the choice of initial conditions. Basins of attractions of various competing attractors display complex basin boundaries thus suggesting possible jumps between coexisting solutions in experiment. Compared to previously published jerk circuits with similar behavior, the novel system distinguishes by the presence of a single equilibrium point and a relatively simpler structure (only off-the-shelf electronic components are involved). Results of theoretical analyses are perfectly traced by laboratory experimental measurements.

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Correspondence to J. Kengne.

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Kengne, J., Negou, A.N. & Tchiotsop, D. Antimonotonicity, chaos and multiple attractors in a novel autonomous memristor-based jerk circuit. Nonlinear Dyn 88, 2589–2608 (2017). https://doi.org/10.1007/s11071-017-3397-1

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Keywords

  • Memristive jerk circuit
  • Bifurcation analysis
  • Antimonotonicity
  • Coexistence of multiple attractors
  • Experimental study