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Jordan, D.W. and Smith, P. (2007) Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers. 4th Edition, Oxford University Press, New York.

has been cited by the following article:

• 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.