3 papers
math.DS2026
On the cyclicity of the period annulus of quasi-homogeneous polynomial vector fields
Lubomir Gavrilov, Hongjin He, Dongmei Xiao
In this article, we study the number of limit cycles, bifurcating from the period annulus of any quasi-homogeneous polynomial vector fields with a center, under a one-parameter pol…
math.DS2025
Linear multiplicative noise destroys a two-dimensional attractive compact manifold of three-dimensional Kolmogorov systems
Dongmei Xiao, Shengnan Yin, Chenwan Zhou
In the paper we first characterize three-dimensional Kolmogorov systems possessing a two-dimensional invariant sphere in , then establish a global attracting criterio…
math.DS2024
Stochastic bifurcation of a three-dimensional stochastic Kolmogorov system
Dongmei Xiao, Deng Zhang, Chenwan Zhou
In this paper we systematically investigate the stochastic bifurcations of both ergodic stationary measures and global dynamics for stochastic Kolmogorov differential systems, whic…