Self-locating control of chaotic systems using Newton algorithm
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2005, Physics Letters, Section A: General, Atomic and Solid State PhysicsCitation Excerpt :This limitation holds for all kinds of DFC methods, including exponential and extended DFC methods [6,7]. Hence overcoming this limitation has been a topic in chaos control field [3,8–16]. So far, many methods have been proposed to resolve this limitation, including the static and dynamic feedback methods [8,12], the optimality principle [9] and Newton algorithm [14].
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2003, Physics Letters, Section A: General, Atomic and Solid State PhysicsEstimation of periodic-like motions of chaotic evolutions using detected unstable periodic patterns
2002, Pattern Recognition LettersCitation Excerpt :The UPOs provide a skeleton for the organization of the complex dynamics, and can be considered one of the major advances in the understanding of the general behavior of a nonlinear dynamical system. There have been some applications of using information of UPO patterns in chaos control (Xu and Bishop, 1996a,b; Bishop and Xu, 1996). UPOs have been also utilized to approximately measure the dimension, and the topological entropy (Lathrop and Kostelich, 1989).