Generating any number of multi-butterfly chaotic attractors via a novel memristor with only one internal function

Due to the distinct nonlinear characteristics and unique memory effects of memristors, they are frequently employed in the fabrication of chaotic systems with intricate dynamics behaviors. However, in most studies, their memristors exhibit two additional internal functional forms, significantly increasing the design complexity. To address this issue, we propose a novel multi-piecewise memristor intended for the construction of memristive multi-butterfly chaotic system (MMBCS). Through the adjustment of the memristor’s intrinsic parameters, we can control the generation of any number of multi-butterfly attractors. Notably, the designed memristor can generate both odd-numbered and even-numbered multi-scroll with only one form of memristive function and state variable function. This feature simplifies design complexity, expanding the potential for chaotic system applications. Dynamics analysis of the MMBCSs is conducted comprehensively, encompassing phase portraits, bifurcation diagrams, and Lyapunov exponents, which confirm their complex chaotic properties. Furthermore, potential applications of the proposed MMBCSs are designed through synchronous control simulation experiments.