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Recurrence-Based Representations of the Logistic Map
Recurrence-Based Representations of the Logistic Map
Recurrence plots and recurrence networks are complementary representations of the recurrence properties of a time series. Every time step constitutes a node of the recurrence network. A recurrence in phase space is either represented by a link in the recurrence network or as a black dot in the recurrence plot. Two time steps are recurrent if and only if their mutual distance is smaller than a threshold .
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The logistic map is a prototypical example for dynamical transitions between regular, laminar, and chaotic behaviors of a dynamical system. The evolution and the dynamical properties of the time series depend on the control parameter .
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