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Stabilizing The Lorenz Flows Using A Closed Loop Quotient Controller, James P. Braselton, Yan Wu
Stabilizing The Lorenz Flows Using A Closed Loop Quotient Controller, James P. Braselton, Yan Wu
Department of Mathematical Sciences Faculty Publications
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.
From Chaos To Order Through Mixing, Dmitriy Dmitrishin, I. M. Skrinnik, Alexander M. Stokolos
From Chaos To Order Through Mixing, Dmitriy Dmitrishin, I. M. Skrinnik, Alexander M. Stokolos
Department of Mathematical Sciences Faculty Publications
In this article we consider the possibility of controlling the dynamics of nonlinear discrete systems. A new method of control is by mixing states of the system (or the functions of these states) calculated on previous steps. This approach allows us to locally stabilize a priori unknown cycles of a given length. As a special case, we have a cycle stabilization using nonlinear feedback. Several examples are considered.
Applying Linear Controls To Chaotic Continuous Dynamical Systems, James P. Braselton, Yan Wu
Applying Linear Controls To Chaotic Continuous Dynamical Systems, James P. Braselton, Yan Wu
Department of Mathematical Sciences Faculty Publications
In this case-study, we examine the effects of linear control on continuous dynamical systems that exhibit chaotic behavior using the symbolic computer algebra system Mathematica. Stabilizing (or controlling) higher-dimensional chaotic dynamical systems is generally a difficult problem, Musielak and Musielak, [1]. We numerically illustrate that sometimes elementary approaches can yield the desired numerical results with two different continuous higher order dynamical systems that exhibit chaotic behavior, the Lorenz equations and the Rössler attractor.