Chaos, bubble-like bifurcations and coexisting behaviors in a first-order memristive diode bridge-based simple self-sustained van der Pol-Duffing’s oscillator

This paper introduces and studies the dynamic behaviors of a newly developed, memristor-based self-sustained van der Pol-Duffing oscillator system. The model is constructed from a basic self-governing circuit configuration with a diode pair by replacing the nonlinear components with a first-order memristive diode bridge. The Kirchhoff’s laws are applied to the circuit to derive its electrical state equations, which are modified to the dimensionless form. The equilibrium states of the model and their stability are analyzed. The dynamic behaviors of the model are studied with the help of phase portraits, bifurcation diagrams, Lyapunov exponents, and cross section of basin of attraction. Computational simulations demonstrate highly intricate and diverse operational regimes, exhibiting regular as well as chaotic trajectories, bubble-bifurcation, and multi-stability where distinct attractors coexist under identical parametric settings but varying initial states. A comparison between the proposed oscillator and ten other related systems featuring the same memristor model (a diode bridge cascaded with a first-order parallel RC filter) is presented. Remarkably, the proposed system achieves the lowest dimension and fewest terms while maintaining rich and complex dynamical behaviors comparable to the existing systems. Experimental observations are carried out via PSpice-based circuit simulations to validate the numerical simulation results.