TITLE:
Stabilizing the Lorenz Flows Using a Closed Loop Quotient Controller
AUTHORS:
James Braselton, Yan Wu
KEYWORDS:
Lorenz Equations, Controller, Stability, Routh-Hurwitz Theorem, Chaos, Strange Attractor
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.6 No.8,
August
31,
2016
ABSTRACT: 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.