Asymmetric coexisting bifurcations and multi-stability in an asymmetric memristive diode-bridge-based Jerk circuit

Abstract

An asymmetric memristive diode-bridge (MDB) emulator is raised to imitate the asymmetric volt-ampere characteristic of a physical memristor. Then, an asymmetric MDB-based Jerk circuit is built and its state equation is derived, upon which the theoretical analysis, MATLAB-based numerical simulations, and hardware measurements are executed to reveal the asymmetric coexisting bifurcations and the phenomenon of multi-stability. The memristive Jerk circuit has three equilibrium points of a pair nontrivial equilibrium points of asymmetric unstable saddle-foci and a zero equilibrium point of unstable saddle-focus, which leads to the occurrence of asymmetric coexisting bifurcations and asymmetric local attraction basins. The asymmetrical bifurcations are numerically disclosed by 1-D/2-D bifurcation plots, Lyapunov spectrum, and phase plane trajectories. Multi-stability with asymmetric coexisting attractors under two sets of system parameters are demonstrated as examples by local attraction basins and phase plane trajectories. Thereafter, experimental circuit prototype employing discrete components is manually welded and hardware measurements are executed to validate the numerical simulations.