5 papers
Global dynamics of planar discrete type-K competitive systems
Zhanyuan Hou
For a continuously differentiable Kolmogorov map defined from the nonnegative orthant to itself, a type-K competitive system is defined. Under the assumptions that the system is di…
Global attraction and repulsion of a heteroclinic limit cycle in three dimensional Kolmogorov maps
Zhanyuan Hou
There is a recent development in the carrying simplex theory for competitive maps: under some weaker conditions a map has a modified carrying simplex (one of the author's latest pu…
On existence and uniqueness of a modified carrying simplex for discrete Kolmogorov systems
Zhanyuan Hou
For a map from to of the form , the dynamical system as a population model is competitive if $\frac{\partial f_…
Permanence criteria for Kolmogorov systems with delays
Zhanyuan Hou
In this paper, a class of Kolmogorov systems with delays are studied. Sufficient conditions are provided for a system to have a compact uniform attractor. Then Jansen's result (J.…
Global Attractor in Competitive Lotka-Volterra Systems
Zhanyuan Hou
For autonomous Lotka-Volterra systems of differential equations modelling the dynamics of n competing species, new criteria are established for the existence of a single point glob…