Design of new chaotic system with multi-scroll attractor by using variable transformation and its application

Multi-scroll chaos exhibits complex dynamic behavior, the method of designing chaotic systems with multi-scroll attractor is an important research topic. Without any theoretical guidance, it is very difficult to obtain a new chaotic system, especially the multi-scroll chaotic system. In this paper, a class of new chaotic systems with n-scroll attractor is investigated by using variable transformation based on nth order polynomial of complex number. The Lyapunov exponent, bifurcation diagram, and topological horseshoe in the Poincar & eacute; cross-section of new chaotic systems are presented to rigorously prove the existence of chaos in the multi-scroll chaotic system with the assistance of computer simulation. Based on the proposed multi-scroll chaotic system, a new encryption algorithm is proposed for image information, and the simulation experiments verify the feasibility and effectiveness of the proposed encryption algorithm.