Four-scroll hyperchaos and four-scroll chaos evolved from a novel 4D nonlinear smooth autonomous system

This Letter presents a novel four-dimensional complex nonlinear autonomous system. This system has very rich dynamics and can exhibit hyperchaos, chaos, quasi-periodic and periodic behavior. Applying two symmetrical initial conditions, this system can generate two coexist double-scroll hyperchaotic attractors. More interestingly, this new system can generate not only a four-scroll hyperchaotic but also a four-scroll chaotic attractor. This nonlinear complex system is analyzed by Lyapunov exponent spectrum, bifurcation diagram and Poincaré mapping.