Analysis of bifurcation mechanism of new hyperchaotic system, circuit implementation, and synchronization

In this paper, a simple hyperchaotic system with only two nonlinear terms is proposed. The complex properties of the system are discussed. The transient chaos and the phenomena of attractor coexistence are reported. In addition, the new system has oscillations with controllable spike numbers and symmetric bursting phenomena with period. The bifurcation mechanism of the new system under the parameter control is analyzed using the fast-slow system, and the system exhibits periodic symmetric Fold/Hopf bursting behavior. Then, the hardware circuit of the new system is implemented to verify the correctness of the numerical simulation. Finally, based on the finite-time synchronization method to control the new system, two synchronization results are obtained: the replacement of fast and slow variables in the system of the original fast-slow system, and the appearance of multiple scales variables in the system that would otherwise have no fast-slow system.