Chaos control in the fractional order logistic map via impulses
Marius-F. Danca, Michal Feckan, Nikolay Kuznetsov
TL;DR
This paper presents a method for controlling chaos in a fractional order logistic map using impulsive control, demonstrating bounded solutions and verifying results through numerical analysis.
Contribution
It introduces an impulsive control algorithm for fractional order logistic maps and analyzes its effectiveness in chaos suppression.
Findings
Solutions remain bounded under impulsive control
Numerical results confirm chaos control effectiveness
Impulsive control modifies bifurcation behavior
Abstract
In this paper the chaos control in the discrete logistic map of fractional order is obtained with an impulsive control algorithm. The underlying discrete initial value problem of fractional order is considered in terms of Caputo delta fractional difference. Every steps, the state variable is instantly modified with the same impulse value, chosen from a bifurcation diagram versus impulse. It is shown that the solution of the impulsive control is bounded. The numerical results are verified via time series, histograms, and the 0-1 test. Several examples are considered
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