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 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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