On asymptotic properties of some complex Lorenz-like systems

TL;DR

This paper investigates the long-term behavior of complex Lorenz-like systems, which are generalizations of the classical Lorenz equations involving complex variables, relevant to physics and fluid dynamics.

Contribution

It provides an analysis of the asymptotic properties of complex Lorenz systems, extending understanding of their behavior in physical models.

Findings

Analysis of stability conditions for complex Lorenz systems

Identification of parameter regimes leading to chaotic behavior

Insights into physical phenomena modeled by these systems

Abstract

The classical Lorenz lowest order system of three nonlinear ordinary differential equations, capable of producing chaotic solutions, has been generalized by various authors in two main directions: (i) for number of equations larger than three (Curry1978) and (ii) for the case of complex variables and parameters. Problems of laser physics and geophysical fluid dynamics (baroclinic instability, geodynamic theory, etc. - see the references) can be related to this second aspect of generalization. In this paper we study the asymptotic properties of some complex Lorenz systems, keeping in the mind the physical basis of the model mathematical equations.