Analysis of a novel 3D autonomous system with intermittent chaos and its finite-time sliding mode synchronization

By improving the Bao system, a new 3D autonomous chaotic system is obtained. This paper analyses the phase diagram, bifurcation diagram, Lyapunov exponents, and complexity of the new system, revealing its rich dynamical behaviours. The new system exhibits extreme sensitivity to both parameters and initial conditions. Specifically, the phenomena of transient chaos, intermittent chaos, and coexisting attractor are discussed. Furthermore, to verify the practical feasibility of the new system, an analogue simulation circuit is designed, and the digital circuit is implemented using the Field Programmable Gate Array (FPGA). The experimental results show that the simulation and actual circuit implementation are consistent with the theoretical analysis, verifying the system’s stability and feasibility. Finally, an improved nonlinear integral Sliding Mode (SM) surface is constructed, and a SM controller is designed based on this surface to achieve synchronous control of chaotic systems with external perturbations. The simulation results align with the theoretical analysis, demonstrating that the proposed SM control method has good control performance and is well-suited for practical applications.