Design and application of multi-scroll chaotic attractors based on simplified Lorenz system

Abstract

Two linear systems are obtained by employing linearization technique in a simplified Lorenz system, and a two-scroll chaotic attractor is generated via the control method. Multi-scroll chaotic attractors are generated by extending the saddle-focus equilibrium points with index 2. Dynamic characteristics of the multi-scroll chaotic system are analyzed by observing the phase diagrams, bifurcation diagrams, Poincaré sections and calculating the largest Lyapunov exponent. A circuit for the multi-scroll attractor is designed and simulated. The numerical simulation result and the circuit simulation result are consistent with each other. To apply the multi-scroll chaotic systems to image encryption, an improved hybrid encryption algorithm is designed based on the multi-scroll chaotic system and advanced encryption standard (AES), and its encryption performances are analyzed. The results show that the improved hybrid encryption has a higher security.