Chaos of the logistic equation with piecewise constant argument
Marat Akhmet, Derya Altintan, Tanil Ergenc
TL;DR
This paper investigates the logistic equation with piecewise constant argument, demonstrating that it can generate chaotic and intermittent behavior through various routes, supported by visualizations of complex dynamics.
Contribution
It proves the occurrence of chaos and intermittency in the logistic equation with piecewise constant argument, including Li-Yorke chaos and period-doubling routes, with illustrative plots.
Findings
The equation exhibits chaos and intermittency.
Li-Yorke chaos is established.
Chaos through period-doubling is demonstrated.
Abstract
We consider the logistic equation with different types of the piecewise constant argument. It is proved that the equation generates chaos and intermittency. Li-Yorke chaos is obtained as well as the chaos through period-doubling route. Basic plots are presented to show the complexity of the behavior.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Nonlinear Dynamics and Pattern Formation · Mathematical Dynamics and Fractals