Power Spectrum of the Logistic Map

The power spectrum shows the energy distribution over different frequencies of a time series The logistic map is a prototypical example for dynamical transitions between regular laminar and chaotic behaviors of a dynamical system The evolution of the time series depends on the control parameter and the initial value The time series is defined by the iterative map Although the time series changes for different initial values with fixed control parameter the power spectrum outside the fixed points stays approximately the same

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