A 3D memristor-based chaotic system with transition behaviors of coexisting attractors between equilibrium points

•The introduction of a smooth memristor in the jerk chaotic system does not increase the dimensionality of the system.•It demonstrates three types of multistablity, including symmetric homogeneous and asymmetric heterogeneous coexistence attractors.•The transition behavior of coexistence attractors between symmetrical equilibrium points is found. A 3D symmetric memristor-based chaotic system (SMCS) is constructed by introducing a smooth quadratic flux control memristor model into the jerk chaotic system (JCS). The dynamics of SMCS are investigated by means of Lyapunov exponents, bifurcation diagrams, multistability, transient behavior, and spectral entropy complexity. It is found that SMCS is sensitive to parameter b included in the normalized equation. Transition behaviors of coexisting attractors between the equilibrium points will be observed when parameter b changes in a specific interval. Its complexity is demonstrated by the types of three multi-stable behaviors and four types of transient behaviors and distinctly enhanced by the spectral entropy complexity as two parameters variations. Additionally, the physical realizability of SMCS is verified by the implementation of the analog circuit and digital hardware. Finally, the pseudo-random sequence based on JCS and SCMS is compared by NIST testing.