Period-Doubling Route to Chaos and Intermittency in a Hybrid R\"ossler Model

TL;DR

This paper investigates how a piecewise constant perturbation, based on the logistic map, induces chaos, period-doubling, and intermittency in a R"ossler system, including coupled systems, revealing the role of discontinuous perturbations in chaos generation.

Contribution

It introduces a novel hybrid R"ossler model with logistic map-based perturbation, demonstrating chaos and bifurcation phenomena due to discontinuous perturbations.

Findings

Discontinuous perturbations induce chaos in the R"ossler system.

Period-doubling cascade observed under specific perturbations.

Intermittency phenomena are numerically demonstrated.

Abstract

A R\"ossler model perturbed with a piecewise constant function is investigated. The perturbation function used in the model is constructed by means of the logistic map. In the absence of the perturbation the system is assumed to possess two equilibrium points one of which is linearly stable. The occurrences of period-doubling cascade and intermittency are numerically investigated. Extensions of the aforementioned phenomena among coupled R\"ossler systems are also shown. Our results reveal that discontinuous perturbations are capable of generating continuous chaos.