Design and application of multiscroll chaotic attractors based on a novel multi-segmented memristor

Introducing memristors into the traditional chaotic system can generate multiscroll chaotic attractors, expanding possibilities for information processing and chaotic applications. This paper first proposes a novel multi-segment memristor model based on a multi-segment linear function. Then, based on the Sprott-B system, one-directional memristive multiscroll chaotic attractors (1D-MMSCAs), 2D-MMSCAs, and 3D-MMSCAs are produced separately, with different numbers of novel memristors introduced. The dynamic behavior of the MMSCAs is analyzed in terms of equilibrium points, Lyapunov exponents and bifurcations, coexisting attractors, and complexity. Lyapunov exponent and bifurcation analysis reveal rich dynamic behavior of the MMSCAs, including period-doubling bifurcations, bursts of chaos, and transient of chaos. The MMSCAs exhibit dynamic phenomena such as coexisting attractors, multistability, and super multistability under different initial conditions. Furthermore, the existence and feasibility of the MMSCAs are verified through circuit simulation. Coexisting attractors generation circuits that can change the initial values of arbitrary state variables are designed. Using an improved Euler algorithm and the STM32 microcontroller, the MMSCAs are digitally implemented, expanding the application scope. Comparative results with other multi-scroll chaotic attractors (MSCAs) demonstrate the advantages of the proposed MMSCAs, including controllable scroll number and direction, simple implementation circuits, and rich dynamic behavior. Finally, the MMSCAs are applied to finite-time synchronization. Simulation results show that the two proposed synchronization schemes in this paper require less time to achieve complete synchronization compared to other synchronization schemes. This characteristic enhances the efficiency and practicality of the proposed synchronization strategy in real-world applications.