Analysis and circuit implementation of a non-equilibrium fractional-order chaotic system with hidden multistability and special offset-boosting
Shaohui Yan, Ertong Wang, Qiyu Wang
Abstract
In order to obtain a system of higher complexity, a new fractional-order chaotic system is constructed based on the Sprott system. It is noteworthy that the system has no equilibrium point yet exhibits chaotic properties and has rich dynamical behavior. Its basic properties are analyzed by Lyapunov exponents, phase diagrams, and smaller alignment index tests. The change of its state is observed by changing parameters and order, during which the new system is found to have intermittent chaos phenomena. Surprisingly, the new proposed system has a special offset-boosting phenomenon, where only a boosting-controller makes the system undergo a multi-directional offset, and the shape of the generated hidden attractor changes. In addition, changing the initial value brings kinds of coexisting attractors in the system, which proves the existence of multistability. Because the new system is very sensitive to the initial value, the complexity of the new system is calculated based on the complexity algorithm, and the initial value with higher complexity is gained by contrast. Finally, the field programmable gate array is used to implement the actual circuit of the new system to verify its feasibility. This system provides an example for the study of fractional-order chaotic systems and a complex system for fractional-order chaotic applications.