Simplify The Lorenz Hyperchaos System Design And Circuit Implementation Of The Research

To improve the security performance of chaotic encryption system, chaotic systems with high complexity are needed to design in chaos secure communication. In this paper, adopting the methods of theory analysis, numerical simulation and circuit experiment, the generation, dynamical characteristics and the circuit implementation of the hyperchaotic systems and multi-wing attractor which based on the simplified Lorenz system were investigated. The results are valuable and significant for chaos study and its application.Based on the simplified Lorenz system that proposed lately, a state feedback controller and a sinusoidal parameter perturbation were applied to generate hyperchaotic behaviors, and the equilibria and stability were analyzed. On this basis, a coordinate transformation and a nonsingular transformation were applied to generate multi-wing attactor, which improves the behavior complexity and structural complexity. It lays a model foundation for the applications of the simplified Lorenz hyperchaotic system.Dynamical characteristics of the simplified Lorenz hyperchaotic systems and multi-wing attractor were analyzed and discussed numerically by means of phase portraits, the Lyapunov exponent spectrums, bifurcation diagrams and Poincare sections. Some typical bifurcations such as period-doubling, tangent bifurcations, pitchfork and homoclinic bifurcations were observed. Interestingly,2-tori and three-attractor coexisting phenomenon happen at some specific parameter values. It establishes a theoretical foundation for the simplified Lorenz hyperchaotic system applications.Adopting the discrete components, the chaotic analog circuits of simplified Lorenz hyperchaotic systems and multi-wing attractor were designed and realized. The system parameters correspond with the circuit variable resistor. By regulating the resistor in the circuit, dynamic behaviors were observed, including period orbits, quasi-period orbits, chaos, four-wing attractor and hyperchaos. Results from circuit experiments, theoretical analysis, and simulations are accordant. It shows that the simplified Lorenz hyperchaotic system has rich dynamical characteristics and physical implementation. It lays a hardware experimental foundation for the simplified Lorenz hyperchaotic system applications in the field of chaotic secure communication.