Chaos in a generalized Lorenz system

TL;DR

This paper investigates chaos and complex dynamics in a generalized Lorenz system, revealing how varying pumping and dissipation lead to stable, unstable, and chaotic regimes with fractal characteristics.

Contribution

It introduces a generalized Lorenz system modeling a quantum cavity device and analyzes its dynamical regimes, including chaos, using divergence and fractal statistics.

Findings

Stable and unstable limit cycles can form with parameter variation.

Transitions to chaos are characterized and detailed.

Chaotic attractors exhibit fractal properties.

Abstract

A three-component dynamic system with influence of pumping and nonlinear dissipation describing a quantum cavity electrodynamic device is studied. Different dynamical regimes are investigated in terms of divergent trajectories approaches and fractal statistics. It has been shown, that in such a system stable and unstable dissipative structures type of limit cycles can be formed with variation of pumping and nonlinear dissipation rate. Transitions to chaotic regime and the corresponding chaotic attractor are studied in details.