Hyperchaos and hyperchaos control of the sinusoidally forced simplified Lorenz system

This paper analyzes the hyperchaotic behaviors of the newly presented simplified Lorenz system by using a sinusoidal parameter variation and hyperchaos control of the forced system via feedback. Through dynamic simulations which include phase portraits, Lyapunov exponents, bifurcation diagrams, and Poincaré sections, we find the sinusoidal forcing not only suppresses chaotic behaviors, but also generates hyperchaos. The forced system also exhibits some typical bifurcations such as the pitchfork, period-doubling, and tangent bifurcations. Interestingly, three-attractor coexisting phenomenon happens at some specific parameter values. Furthermore, a feedback controller is designed for stabilizing the hyperchaos to periodic orbits, which is useful for engineering applications.

Ref: K. Sun, X. Liu, C. Zhu, and  J. C. Sprott, Nonlinear Dynamics 69, 1383-1391 (2012)