A 5D Multi-Stable System with Wide Range of Hyperchaotic States

Large-scale chaotic systems are often used in secure communication and other fields, because they can provide a wider chaotic interval. Most of the existing large-scale chaotic systems are three-dimensional and four-dimensional systems. In order to obtain more chaotic and more complex systems, this study proposed a five-dimensional system with a large range of hyperchaotic states and multiple coexisting attractors. The dynamic characteristics of the five-dimensional system were analyzed by means of coexistence bifurcation diagram,coexistence phase diagram, Lyapunov exponent spectrum and calculation of system divergence. The results show that: the system is a dissipative hyperchaotic system; when the parameters are fixed, the system can produce multiple coexisting attractors only by changing the initial value, and when the parameter d takes different values,the system will produce 12 types of coexistence phenomena, which are period-1 attractor, period-2 attractor, period-4 attractor, quasi-periodic attractor, one-scroll attractor, double-scroll attractor and so on; when the parameter m varies in the range of [0.1, 4000], the system will always maintain a hyperchaotic state, and when m is in the range of [70, 4000], the Lyapunov exponent spectrum of the system remains unchanged and maintains a hyperchaotic state with three positive Lyapunov exponents, indicating that the system has an invariant Lyapunov exponent characteristic. FPGA (field programmable gate array) was used to realize the digital circuit, and the experimental results were observed on the oscilloscope, which verified the feasibility of the hyperchaotic system.