Admissible perturbations of a generalized Langford system

TL;DR

This paper identifies specific perturbations for a generalized Langford system that preserve key qualitative behaviors, demonstrating stability, periodic solutions, and chaotic attractors through both theoretical analysis and numerical simulation.

Contribution

It introduces a class of admissible perturbations for a generalized Langford system that maintain its fundamental dynamical properties.

Findings

Perturbed systems retain original system's qualitative properties.

Lyapunov instability of equilibrium points is preserved.

Chaotic attractors are observed in both original and perturbed systems.

Abstract

Admissible perturbations (i.e., perturbations that do not change the Mironenko reflecting function of the system) are obtained for an autonomous three-dimensional quadratic generalized Langford system with five parameters. The obtained non-autonomous perturbed systems retain many of the qualitative properties of solutions of the original system. In particular, the instability (in the sense of Lyapunov) of the equilibrium point, the presence of a periodic solution and its asymptotic stability (instability) are proved for perturbed systems. The presence of similar chaotic attractors in the original and perturbed systems is shown by numerical simulation.