The First Integrals and Related Properties of a Class of Quintic Systems with a Uniform Isochronous Center (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we give all the first integrals of the quintic systemswhich have a uniform isochronous center, and use them to determine the qualitative behavior of the periodic solutions of their equivalent non-autonomoussystems. Meanwhile, we clearly describe the local phase portraits of singularityat infinity.