Chaotifying a continuous-time system near a stable limit cycle

Abstract This paper studies the chaotification problem of driving a continuous-time system chaotic near its stable limit cycle. The controller is designed to ensure the controlled orbit be bounded and, meanwhile, have positive Lyapunov exponents. A numerical example is given to illustrate the effectiveness of the proposed chaotification algorithm.

[1]  W. Ditto,et al.  Controlling chaos in the brain , 1994, Nature.

[2]  Schwartz,et al.  Tracking sustained chaos: A segmentation method , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  Ying-Cheng Lai,et al.  Controlling chaos , 1994 .

[4]  Guanrong Chen,et al.  Feedback anticontrol of discrete chaos , 1998 .

[5]  Xinghuo Yu,et al.  Anticontrol of chaos in continuous-time systems via time-delay feedback. , 2000, Chaos.

[6]  Guanrong Chen,et al.  Chaotifying a Continuous-Time System via impulsive Input , 2002, Int. J. Bifurc. Chaos.

[7]  S. Čelikovský,et al.  Control systems: from linear analysis to synthesis of chaos , 1996 .

[8]  Guanrong Chen.  Controlling Chaos and Bifurcations in Engineering Systems , 1999 .

[9]  Guanrong Chen,et al.  FEEDBACK CONTROL OF LYAPUNOV EXPONENTS FOR DISCRETE-TIME DYNAMICAL SYSTEMS , 1996 .

[10]  Alexander L. Fradkov,et al.  Introduction to Control of Oscillations and Chaos , 1998 .

[11]  Ott,et al.  Preserving chaos: Control strategies to preserve complex dynamics with potential relevance to biological disorders. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  Guanrong Chen,et al.  Chaotification via arbitrarily Small Feedback Controls: Theory, Method, and Applications , 2000, Int. J. Bifurc. Chaos.

[13]  M. Lakshmanan,et al.  Chaos in Nonlinear Oscillators: Controlling and Synchronization , 1996 .