IDENTIFYING REPEATING PATHS WITH CRITICAL VALUES, ANALYZING TIME SERIES DATA, CALCULATING THE LYAPUNOV EXPONENT AND MANAGING CHAOS IN CHAOTIC SYSTEMS

Nilima Dutta

Abstract


Period doubling bifurcations have been observed in many different dynamical systems, both dissipative and conservative, since Feigenbaum’s first discovery. The theory behind this phenomenon has been widely studied. In this paper, we investigate three characteristics of a nonlinear chaotic system described by the equation    , where p represents the control parameter as given below:

1) We first analyze the range of the function and establish a general pathway from the stable system to the chaotic region by applying Feigenbaum's theory of period doubling bifurcations.

2) We determine the accumulation point at p = 3.2146537697423 and the Feigenbaum constant


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