q-deformed logistic map with delay feedback

TL;DR

This paper investigates how q-deformations and delay feedback influence the stability and chaos in logistic maps, revealing parameter regions where chaos is suppressed or recovered, with implications for controlling complex systems.

Contribution

It introduces and analyzes two types of q-deformations in delay logistic maps, exploring their effects on stability, bifurcations, and chaos suppression or recovery.

Findings

Chaos can be suppressed in certain deformation and delay parameter regions.

Steady states are maintained in one deformation type with delay feedback.

Chaotic behavior re-emerges with increasing delay in the other deformation type.

Abstract

The delay logistic map with two types of q-deformations: Tsallis and Quantum-group type are studied. The stability of the map and its bifurcation scheme is analyzed as a function of the deformation and delay feedback parameters. Chaos is suppressed in a certain region of deformation and feedback parameter space. The steady state obtained by delay feedback is maintained in one type of deformation while chaotic behavior is recovered in another type with increasing delay.