5 papers
Global dynamics of three-dimensional Lotka-Volterra competition models with seasonal succession: II. Uniqueness of positive fixed points
Lei Niu, Yi Wang, Xizhuang Xie
In this second part of the series, we investigate the uniqueness of positive fixed points of the Poincare map associated with the 3-dimensional Lotka-Volterra competition model wit…
Classification of permanence and impermanence for a Lotka-Volterra model of three competing species with seasonal succession
Lei Niu, Xizhuang Xie
In this paper, we are concerned with the permanence of a Lotka-Volterra model of three competing species with seasonal succession. Based on the existence of a carrying simplex, tha…
Global dynamics of three-dimensional Lotka-Volterra competition models with seasonal succession: I. Classification of dynamics
Lei Niu, Yi Wang, Xizhuang Xie
The current series of two papers focus on a 3-dimensional Lotka-Volterra competition model of differential equations with seasonal succession, which exhibits that populations exper…
Heteroclinic Cycles of A Symmetric May-Leonard Competition Model with Seasonal Succession
Xizhuang Xie, Lin Niu
In this paper, we are concerned with the stability of heteroclinic cycles of the symmetric May-Leonard competition model with seasonal succession. Sufficient conditions for stabili…
Generic Poincaré-Bendixson Theorem for singularly perturbed monotone systems with respect to cones of rank-
Lin Niu, Xizhuang Xie
We investigate the singularly perturbed monotone systems with respect to cones of rank and obtain the so called Generic Poincaré-Bendixson theorem for such perturbed systems, t…