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A study on global stabilization of periodic orbits in discrete-time chaotic systems by using symbolic dynamics. (English) Zbl 1340.37008
Summary: In this report, a control method for the stabilization of periodic orbits for a class of one- and two-dimensional discrete-time systems that are topologically conjugate to symbolic dynamical systems is proposed and applied to a population model in an ecosystem and the Smale horseshoe map. A periodic orbit is assigned as a target by giving a sequence in which symbols have periodicity. As a consequence, it is shown that any periodic orbits can be globally stabilized by using arbitrarily small control inputs. This work is a new attempt to systematically design a control system based on symbolic dynamics in the sense that one estimates the magnitude of control inputs and analyzes the Lyapunov stability.
##### MSC:
 37B10 Symbolic dynamics 74H65 Chaotic behavior of solutions to dynamical problems in solid mechanics 93D15 Stabilization of systems by feedback
##### Keywords:
symbolic dynamics; chaos control; global stability
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##### References:
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