Dynamical analysis and finite-time synchronization of grid-scroll memristive chaotic system without equilibrium

The study of multi-scroll memristive chaotic system has attracted great interest due to their unique dynamics. In this paper, a novel five-dimensional chaotic system devoid of equilibria is constructed by introducing two memristors into a three-dimensional chaotic system, resulting in the emergence of a grid-scroll attractor. The evolution of the chaotic system is analyzed using techniques such as phase diagrams, Poincare maps, bifurcation diagrams, and Lyapunov exponents. The basin of attraction is delineated to investigate the coexisting attractors in the system. By manipulating the parameters, the partial amplitude of the system can be modulated. To experimentally confirm the existence of the proposed system, a circuit is meticulously designed and implemented. At last, an adaptive controller is designed, and it is observed from the simulation results that a synchronization state can be reached by the two chaotic systems within a finite time.