A new chaotic system with nested coexisting multiple attractors and riddled basins

This paper presents a new three-dimensional chaotic system with a nonlinear term. More interesting is that the system can produce different types of coexisting attractors under one sets of fixed model parameters, which include point attractor, bursting orbit, three kinds of period orbits, and two kinds of chaotic orbits. At the same time, the coexisting attractors have nested structure. In addition, riddled basins are observed on local attraction basins, which indicate that the dynamical behaviors of proposed system are extremely sensitive to the initial conditions. Finally, by setting different initial condition, the circuit can generate multitudinous coexisting attractors. The circuit implementation in Pspice supports furtherly numerical analyses and validates the mathematical model.