Various coexisting attractors, asymmetry analysis and multistability control in a 3D memristive jerk system

In this paper, the dynamics of a 3D memristive jerk oscillator is investigated both analytically and numerically with the help of Routh-Hurwitz criteria, phase portraits, bifurcation diagrams, and basins of attraction. The analyses show that the system is bistable because of its inversion symmetry. In addition, the system enters chaos by period-doubling bifurcation. It has a double-scroll chaotic attractor (as a result of mixing two bistable chaotic attractors). More interestingly, multistability involving the coexistence of multiple stable states (i.e., four and up to six coexisting attractors) is found when monitoring the system parameters and initial conditions. Furthermore, the state control from multistability to monostability is performed using the linear augmentation scheme. We also address the realistic issue of symmetry-breaking by considering an asymmetric memristive device. The asymmetry analysis produces two asymmetric coexisting bifurcation diagrams (i.e., asymmetric bi-stability) each of which exhibits its own sequence of bifurcations to chaos when monitoring the main control parameter. The PSpice circuit simulation results match well with the theoretical and numerical results. Finally, the microcontroller-based experimental implementation is carried out to verify the analytical and numerical studies. To the best of our knowledge, we would like to stress that the results obtained in this paper are unique and of great importance for developing and the understanding of memristive devices-based systems.