No-argument memristive hyper-jerk system and its coexisting chaotic bubbles boosted by initial conditions

Abstract

Abstract Antimonotonicity is used to characterize the specific dynamics for the generation of periodic orbits cascaded by their destruction, which is generally involved with the change of a bifurcation parameter. However, this phenomenon of antimonotonicity is rarely induced by the initial conditions of chaotic systems. To this end, this paper presents a no-argument memristive hyper-jerk system. When taking the initial condition of the memristor inner state (called as “memristor initial condition” for short) as a bifurcation parameter, we disclose the chaotic bubbles located in the primary interval and thereby display the coexisting infinitely many attractors with extreme multi-stability. Afterwards, when switching the memristor initial condition, we also uncover the initial condition-boosted coexisting chaotic bubbles theoretically and numerically. Therefore, the complex phenomenon of the extreme multi-stability with the initial condition-boosted coexisting chaotic bubbles is well revealed. Furthermore, a reconstituted model with the initial conditions in an explicit form is established in integral domain and the extreme multi-stability can be effectively interpreted through the stability analysis of the determined equilibrium points of the reconstituted model. Finally, a digital hardware platform is implemented to verify the memristor initial condition-dependent chaotic bubbles.