# Power Spectrum of the Logistic Map

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 =a(1-).

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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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