Fast cycles detecting in non-linear discrete systems

TL;DR

This paper proposes a generalized nonlinear delayed feedback control scheme to enhance the detection speed of unstable periodic orbits in non-linear autonomous discrete systems, supported by numerical simulations.

Contribution

It introduces a novel generalization of the nonlinear DFC scheme specifically aimed at improving T-cycle detection rates.

Findings

Enhanced detection speed of T-cycles demonstrated

Generalized nonlinear DFC scheme effective in simulations

Applicable to stabilization of unknown unstable orbits

Abstract

In the paper below we consider a problem of stabilization of a priori unknown unstable periodic orbits in non-linear autonomous discrete dynamical systems. We suggest a generalization of a non-linear DFC scheme to improve the rate of detecting T-cycles. Some numerical simulations are presented.