This paper dealt with the existence of periodic waves for a perturbed quintic BBM equation
by using geometric singular perturbation theory. By analyzing the perturbations of the …

This paper concerns the exact bound on the number of zeros of Abelian integrals associated
with two hyper-elliptic Hamiltonian systems of degree 4. The upper and lower bounds for the …

This paper deals with the maximum number of limit cycles, which can be bifurcated from
periodic orbits of planar piecewise smooth Hamiltonian systems, which are located in a …

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In this paper, we study the number of isolated zeros of Abelian integrals associated to
system x˙= y, y˙=− x 3 (x 2− 1) 2 under the perturbations of ϵ (α 0+ α 1 x 2+ α 2 x 4+ α 3 x 6) …

In this paper, we study the bound of the number of limit cycles by Poincaré bifurcation for a
Liénard system of type (4, 3). An automatic algorithm is constructed based on the …

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 …

In this work we consider cuspidal loops, ie, homoclinic orbits to cuspidal singular points. We
develop an iterative procedure, founded on the nonlinear time transformation method, to …

In this paper, we consider the upper bounds of a number of isolated zeros of Abelian
integrals associated to system x ̇= y, y ̇=− x 3 (x 2− 1) under the perturbations of ϵ (α 0+ α …

In this article, we study four Abelian integrals over compact level curves of four sixth-degree
hyper-elliptic Hamiltonians with parameters. We prove that the sharp bound of the number of …