A New Four-Dimensional Chaotic System with Multistability and Its Predefined-Time Synchronization

Abstract

A new chaotic system is obtained by modifying the Sprott-C system. Then the phase diagrams, power spectra, 0–1 tests, Poincaré maps, Lyapunov exponential spectra, time sequences, and complexity are studied. Research indicates that the system is sensitive to parameters and initial conditions, and bursting oscillation, transient chaos and multistability are investigated. The complexity of the new system is calculated using the Sample Entropy (SE) complexity algorithm, including selecting more suitable initial values and parameters for the application. In addition, the system circuit designed by Multisim and the actual digital circuit realized by Field Programmable Gate Array (FPGA) verify the feasibility of the system. Finally, to obtain a more appropriate synchronization result for practical applications, a synchronous controller is designed to successfully implement the predefined-time synchronization of the system in different dimensions. The simulation results demonstrate that the predefined-time synchronization can control the synchronous time and is unaffected by the initial conditions. The results demonstrate that this synchronization method is well accommodated to practical applications.