Hidden chaotic attractors and chaos suppression in an impulsive discrete economical supply and demand dynamical system

TL;DR

This paper demonstrates how impulsive control can suppress chaos in a discrete supply and demand system, revealing hidden chaotic attractors and providing analytical proofs of bounded, periodic orbits.

Contribution

It introduces a novel impulsive control method that not only suppresses chaos but also uncovers hidden chaotic attractors in discrete dynamical systems.

Findings

Impulsive control effectively suppresses chaos in the system.

Hidden chaotic attractors can be generated by impulsive difference equations.

Analytical proofs confirm boundedness and periodicity of orbits.

Abstract

Impulsive control is used to suppress the chaotic behavior in an one-dimensional discrete supply and demand dynamical system. By perturbing periodically the state variable with constant impulses, the chaos can be suppressed. It is proved analytically that the obtained orbits are bounded and periodic. Moreover, it is shown for the first time that the difference equations with impulses, used to control the chaos, can generate hidden chaotic attractors. To the best of the authors knowledge, this interesting feature has not yet been discussed. The impulsive algorithm can be used to stabilize chaos in other classes of discrete dynamical systems.