Complicated Attractor and Novel Route to Chaos via Cubic Nonlinearity Controller

By introducing a nonlinear state feedback controller, a complicated chaotic attractor of four- dimensional continuous autonomous chaotic system evolved from Lorenz system is proposed. The controller consists of a cubic cross-product term of three variables and a self variable term with control parameter. This paper verifies that the proposed system has complex dynamical behavior, which can evolve into periodic and chaotic behavior cyclically. These circular routes to chaos have self-similar bifurcation structure in a wide parameter variation range. An electronic circuit is designed to demonstrate the complicated attractor.