A nonlinear system which exhibits a strange attractor is considered, with the goal of illustrating how to control the chaotic dynamical system and how to obtain a desired attracting periodic orbit by the OGY control a...A nonlinear system which exhibits a strange attractor is considered, with the goal of illustrating how to control the chaotic dynamical system and how to obtain a desired attracting periodic orbit by the OGY control algorithm.展开更多
This paper presents a method for the generation of satisfied strange attractor images, which is based on the idea of Genetic Algorithm and is realized by adding a controller to a chaotic system.The principle of the me...This paper presents a method for the generation of satisfied strange attractor images, which is based on the idea of Genetic Algorithm and is realized by adding a controller to a chaotic system.The principle of the method is introduced. Some problems which exist in genetic algorithm’s parameter optimization are discussed in detail. Finally, the effectiveness of the method for finding pretty strange attractors is verified. It is helpful to pattern design and works of arts and crafts.展开更多
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 h...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.展开更多
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-di...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.展开更多
文摘A nonlinear system which exhibits a strange attractor is considered, with the goal of illustrating how to control the chaotic dynamical system and how to obtain a desired attracting periodic orbit by the OGY control algorithm.
文摘This paper presents a method for the generation of satisfied strange attractor images, which is based on the idea of Genetic Algorithm and is realized by adding a controller to a chaotic system.The principle of the method is introduced. Some problems which exist in genetic algorithm’s parameter optimization are discussed in detail. Finally, the effectiveness of the method for finding pretty strange attractors is verified. It is helpful to pattern design and works of arts and crafts.
文摘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.
文摘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.
