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

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.