Cyclicity of centers on center manifolds in a 3D chaotic system with a four-wing attractor

TL;DR

This paper analyzes the conditions for the existence of centers and limit cycles on the center manifold of a new 3D chaotic system, improving bounds on bifurcating limit cycles from Hopf points.

Contribution

It provides new criteria for centers and cyclicity on the center manifold, enhancing understanding of bifurcations in a recently introduced chaotic system.

Findings

Improved lower bound on the number of bifurcating limit cycles.

Solved the center-focus problem for specific Hopf points.

Analyzed isochronicity and cyclicity of the system.

Abstract

In this work, we investigate the conditions that guarantee the existence of centers on the center manifold, arising from Hopf points, in the new three-dimensional quadratic chaotic system introduced by B. Khaled et al. in 2024 in the Int. J. Data Netw. Sci. For some of the Hopf points of the system, we solve the center-focus problem on the center manifold, analyzing both its isochronicity and cyclicity. Our results significantly improve the previously known lower bound on the number of limit cycles bifurcating from Hopf points in this system, as established by B. M. Mohammed in 2025 in the Int. J. Bifurc. Chaos Appl. Sci. Eng.