Author(s)

James Braselton, Yan Wu

Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, USA.

In this study, we introduce a closed loop quotient controller into the three-dimensional Lorenz system. We then compute the equilibrium points and analyze their local stability. We use several examples to illustrate how cross-sections of the basins of attraction for the equilibrium points look for various parameter values. We then provided numerical evidence that with the controller, the controlled Lorenz system cannot exhibit chaos if the equilibrium points are locally stable.

Lorenz Equations, Controller, Stability, Routh-Hurwitz Theorem, Chaos, Strange Attractor

Braselton, J. and Wu, Y. (2016) Stabilizing the Lorenz Flows Using a Closed Loop Quotient Controller. Open Journal of Applied Sciences, 6, 560-578. doi: 10.4236/ojapps.2016.68056.