Polynomial law for controlling the generation of n-scroll chaotic attractors in an optoelectronic delayed oscillator

TL;DR

This paper explores how to control the number of scroll chaotic attractors in an optoelectronic oscillator by adjusting feedback strength, enabling transitions from simple to complex multi-scroll states with characterized dynamics.

Contribution

It introduces a method to generate and control arbitrary n-scroll attractors in an optoelectronic oscillator using polynomial laws and feedback adjustment.

Findings

Transition from Van der Pol-like to 6-scroll attractors demonstrated

Feedback strength controls the number of scrolls

Lyapunov exponents and autocorrelation coefficients characterize state complexity

Abstract

Controlled transitions between a hierarchy of n-scroll attractors are investigated in a nonlinear optoelectronic oscillator. Using the system's feedback strength as a control parameter, it is shown experimentally the transition from Van der Pol-like attractors to 6-scroll, but in general, this scheme can produce an arbitrary number of scrolls. The complexity of every state is characterized by Lyapunov exponents and autocorrelation coefficients.