Coexisting bifurcations in a memristive hyperchaotic oscillator

This paper investigates the dynamical behavior of the Tamasevicius et al. (1997) oscillator (named TCMNL hereafter) considering memristor as the nonlinear element by replacing the single diode in the original circuit. Various methods for detecting chaos/hyperchaos including bifurcation diagrams, spectrum of Lyapunov exponent, two parameter Lyapunov exponent, Poincare sections and phase portraits are exploited to establish the connection between the system parameters and various complicated dynamics. By tuning the system parameters, some striking phenomena such as quasi -periodic oscillations and asymmetric pair of stable/unstable attractors are depicted. It is also found that the considered memristor induces the phenomenon of coexistence of attractors in wide ranges of bifurcation parameter. Finally, the hardware circuit is implemented and experimental observations are found to be in good agreement with the numerical investigations.