Resonant Y-shaped soliton solutions to the Kadomtsev–Petviashvili II (KPII) equation are
modelled as shock solutions to an infinite family of modulation conservation laws. The fully …

The classical theory of Kosambi–Cartan–Chern (KCC) developed in differential geometry
provides a powerful method for analyzing the behaviors of dynamical systems. In the KCC …

This paper provides a survey on symbolic computational approaches for the analysis of
qualitative behaviors of systems of ordinary differential equations, focusing on symbolic and …

This paper introduces an algorithmic approach to the analysis of bifurcation of limit cycles
from the centers of nonlinear continuous differential systems via the averaging method. We …

This paper is devoted to the study of infinitesimal limit cycles that can bifurcate from zero-
Hopf equilibria of differential systems based on the averaging method. We develop an …

We consider quadratic three-dimensional differential systems having a Hopf singular point.
We study their cyclicity when the singular point is a center on the center manifold using …

We study integrability and bifurcations of a three-dimensional circuit differential system. The
emerging of periodic solutions under Hopf bifurcation and zero-Hopf bifurcation is …

This work deals with three current and relevant problems in the qualitative theory of
differential equations. The first one is the center problem on a center manifold of differential …

Rigid centres on the center manifold of tridimensional differential systems Page 1 Proceedings
of the Royal Society of Edinburgh, 152, 1058–1080, 2022 DOI:10.1017/prm.2021.46 Rigid …

One of the main open problems in the qualitative theory of real planar differential systems is
the study of limit cycles. In this article, we present an algorithmic approach for detecting how …