A New Hyperchaotic System and Its Point Multiplication Combination Synchronization

This paper constructs a new 7-dimensional hyperchaotic system. The hyperchaotic system has two positive Lyapunov exponents and rich chaotic dynamics. Based on the Matlab simulation software, the dynamic behavior of the hyperchaotic system is analyzed, such as phase diagram, dissipativity, equilibrium point, Lyapunov exponent, etc. The simulation results show that the system can produce periodic orbits, chaotic attractors, hyperchaotic attractors and other rich dynamic behaviors with changes of parameters. According to the vector dot product operation, a new point multiplication combination synchronization method is defined. Based on the Lyapunov stability theorem, a nonlinear controller is designed to realize point multiplication combination synchronization between two drive systems and one response system. Numerical simulations of the new hyperchaotic system verify the correctness of the theoretical analysis.