A chaotic system with attractor coexistence and its synchronization circuit implementation

Abstract

We construct a three-dimensional chaotic system based on TANG chaotic system and analyze the system dynamics based on the equilibrium points, phase diagram, Lyapunov exponential spectrum, bifurcation diagram, and complexity. The more complexly dynamic behaviors indicate that our designed system has different topology, bifurcation anti-monotonic property and attractor coexistence phenomenon from TANG system. The system has the coexistence of chaotic attractor and point attractor and can select the initial value that is suitable for chaotic secure communication by analyzing the coexistence attractor. The actual digital circuit is implemented with field programmable gate array (FPGA). The system is extremely sensitive to the selections of initial values and system parameters and has good and rich dynamic behavior, which is suitable for the field of chaotic confidential communication. The linear feedback method is used to control the system synchronous and the simulation of synchronous circuit is realized by Multisim software. The simulation results are consistent with the numerical analysis, which lays a theoretical foundation for the application of the system in the field of synchronized confidential communication.