Four-dimensional system with torus attractor birth via saddle-node bifurcation of limit cycles in content of family of blue sky catastrophes

TL;DR

This paper introduces a new four-dimensional dynamical system exhibiting quasi-periodic behavior, where a torus attractor emerges through saddle-node bifurcation, expanding understanding of blue sky catastrophes and bifurcation phenomena.

Contribution

The study presents a novel four-dimensional model demonstrating torus attractor formation via saddle-node bifurcation within blue sky catastrophe families.

Findings

Torus attractor originates via saddle-node bifurcation.

Torus birth also occurs through Neimark-Sacker bifurcation.

Model exhibits quasi-periodic dynamics in a four-dimensional setting.

Abstract

A new four-dimensional model with quasi-periodic dynamics is suggested. The torus attractor originates via the saddle-node bifurcation, which may be regarded as a member of a bifurcation family embracing different types of blue sky catastrophes. Also the torus birth trough the Neimark-Sacker bifurcation occurs in some other region of the parameter space.