Changjian Liu

collaborators

4 papers

math.DS2024

Stability for a family of planar systems with nilpotent critical points

Ziwei Zhuang, Changjian Liu

Consider a family of planar polynomial systems $x ˙ = y^{2 l - 1} - x^{2 k + 1}, y ˙ = - x + m y^{2 s + 1},$ where $l, k, s \in N^{*},$ $2 \leq l \leq 2 s$ and $m \in R .$ We study…

math.DS2023

On the non-existence of isochronous centers in planar discontinuous differential systems

Ali Bakhshalizadeh, Changjian Liu, Alex C. Rezende

The determination of whether a center is isochronous or not is a well-known problem in the qualitative theory of planar systems. In this paper, we explore planar piecewise disconti…

math.CA2023

Maximum number of limit cycles for Abel equation having coefficients with linear trigonometric functions

Xiangqin Yu, Jianfeng Huang, Changjian Liu

This paper devotes to the study of the classical Abel equation $\frac{d x}{d t} = g (t) x^{3} + f (t) x^{2}$ , where $g (t)$ and $f (t)$ are trigonometric polynomials of degree $m \geq 1$ . We are…

math.CA2023

The number of limit cycles of Josephson equation

Xiangqin Yu, Hebai Chen, Changjian Liu

In this paper, the existence and number of non-contractible limit cycles of the Josephson equation $β \frac{d ^{2} Φ}{d t ^{2}} + (1 + γ cos Φ) \frac{d Φ}{d t} + sin Φ = α$ are studied, where $ϕ\…