A novel chaotic system with a closed curve of four quarter-circles of equilibrium points: dynamics, active backstepping control, and electronic circuit implementation

Abstract In this chapter, we introduce a novel chaotic system with a closed curve consisting of four quarter circles of equilibrium points. The equilibrium curve is symmetric about the straight lines x = ± y . Thus, the new chaotic system exhibits hidden chaotic attractor. The complex behavior of the new chaotic system has been verified by using phase portraits and Lyapunov exponents. We also show that the new chaotic system has multistability and coexisting chaotic attractors for different initial conditions. As control applications, active backstepping-based controllers are designed for the global chaotic stabilization and synchronization of the new chaotic system with four quarter circles of equilibrium points. Furthermore, a theoretical model of the new chaotic system has been converted to an electronic circuit using Kirchhoff's laws and operational amplifiers theory. In addition, the simulation results obtained with the Multisim circuit design show a good match with the simulation results obtained with MATLAB for the theoretical chaotic model.