Designer dynamics through chaotic traps: Controlling complex behavior in driven nonlinear systems

TL;DR

This paper introduces a novel control method for driven nonlinear systems that traps dynamics near any desired trajectory using a chaos-induced order mechanism, enabling simple and experimentally feasible control.

Contribution

It presents a new control paradigm based on chaos-induced trapping near desired trajectories, differing from traditional stabilization methods.

Findings

The control scheme effectively traps system dynamics close to target trajectories.

The method produces chaotic sequences that facilitate the trapping process.

The approach is simple and suitable for experimental implementation.

Abstract

Control schemes for dynamical systems typically involve stabilizing unstable periodic orbits. In this paper we introduce a new paradigm of control that involves `trapping' the dynamics arbitrarily close to any desired trajectory. This is achieved by a state-dependent dynamical selection of the input signal applied to the driven nonlinear system. An emergent property of the trapping process is that the signal changes in a chaotic sequence: a manifestation of chaos-induced order. The simplicity of the control scheme makes it easily implementable in experimental systems.