A Multi-Scroll Memristive Chaotic System via Fractal Process

Fractal theory is a leading and important branch of nonlinear science, which has been widely studied in many fields in the past few decades. Memristor is a nanoscale element with low power consumption and high integration, when it works as the nonlinear part in a chaotic system, the complexity of the chaotic system will be enhanced. Compared with single-scroll chaotic attractor, multi-scroll chaotic attractor have higher complexity and better adaptability. In this paper, the fractal process is applied to a known memristive chaotic system, which can generate multi-scroll chaotic attractor. At first, a fractal iteration is applied to the memristive chaotic system to generate new chaotic attractor. Secondly, the multi-scroll chaotic system is obtained by combining the Julia fractal and memristive chaotic system. And by changing a complex constant in the fractal process, a fractal graph with different shapes is obtained, which can also be used to generate different chaotic attractors in the generating multi-scroll memristive chaotic system. Compared with other multi-scroll chaotic attractors, the proposed multi-scroll chaotic attractors are easier to adjust the number of the scrolls. It can be seen from the simulation diagram that the size of the system phase diagram becomes smaller and smaller as the number of scrolls increases. The results show that the new system has a lot of dynamic characteristics.