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LOGISTIC MAP OF PERIOD-DOUBLING BIFURCATION LEADING TO CHAOS AND ITS CONTROLLER DESIGN

Xiao Wang

Abstract

The period double bifurcation leading to chaos of Logistic map is discussed in detail. The chaos behavior of Logistic Map for μ =4 is proven according to the chaos definition of Devaney for discrete system. A simple chaos control method is presented based on the feedback control principle. The results of simulation show that the performance of the presented chaos control method is better than that of the inverse system method in whether to constant control or to following control.

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Key concepts: Logistic map, CHAOS (operating system), Bifurcation, Control of chaos, Period-doubling bifurcation, Control theory (sociology), Mathematics, Constant (computer programming)