Coexisting oscillations and four-scroll chaotic attractors in a pair of coupled memristor-based Duffing oscillators: Theoretical analysis and circuit simulation

Abstract

We introduce a new four-scroll chaotic system consisting of two autonomous Duffing oscillators with memristive nonlinearity. The memristor emulator consists of a diode bridge and a first-order RC filter. The analytical study of the coupled system shows that it is dissipative, symmetric, and has nine equilibrium points. By using some chaos characterization tools such as bifurcation diagrams, Lyapunov exponent graphs, phase portraits, power spectra, and Poincaré sections, a plethora of dynamical behaviors, such as the period doubling scenario to chaos as well as multistability, are obtained and illustrated. We demonstrate that the system can generate mono-scroll, double-scroll, and four-scroll chaotic attractors according to the coupling parameter. Basins of attraction (illustrating the scenario to four-scroll chaotic attractor) as well as two-parameter Lyapunov diagrams (illustrating the dynamics of the system) are obtained and depicted. To ensure that the new system is implementable, an electronic circuit emulating the model is built and simulated in the PSpice environment.