Periodic orbits, basins of attraction and chaotic beats in two coupled Kerr oscillators

TL;DR

This paper investigates the dynamics of two coupled Kerr oscillators, demonstrating control over their transition between periodic and chaotic states, analyzing stability via Lyapunov maps, and comparing basins of attraction with single Kerr systems.

Contribution

It introduces methods to control and switch the dynamics of coupled Kerr oscillators, including transitions between periodic and chaotic behaviors, and compares their basins of attraction with single systems.

Findings

Control of system dynamics between periodic and chaotic states.

Identification of stable periodic states and their switching.

Comparison of basins of attraction for coupled and single Kerr oscillators.

Abstract

Kerr oscillators are model systems which have practical applications in nonlinear optics. Optical Kerr effect i.e. interaction of optical waves with nonlinear medium with polarizability $\chi^{(3)}$ is the basic phenomenon needed to explain for example the process of light transmission in fibers and optical couplers. In this paper we analyze the two Kerr oscillators coupler and we show that there is a possibility to control the dynamics of this system, especially by switching its dynamics from periodic to chaotic motion and vice versa. Moreover the switching between two different stable periodic states is investigated. The stability of the system is described by the so-called maps of Lyapunov exponents in parametric spaces. Comparison of basins of attractions between two Kerr couplers and a single Kerr system is also presented.