Carrying simplices in nonautonomous and random competitive Kolmogorov systems
نویسندگان
چکیده
The purpose of this paper is to investigate the asymptotic behavior of positive solutions of nonautonomous and random competitive Kolmogorov systems via the skew-product flows approach. It is shown that there exists an unordered carrying simplex which attracts all nontrivial positive orbits of the skewproduct flow associated with a nonautonomous (random) competitive Kolmogorov system. © 2008 Elsevier Inc. All rights reserved. MSC: 34C12; 34D45; 37B55; 37H10; 37N25; 92D25
منابع مشابه
Geometry of carrying simplices of 3-species competitive Lotka-Volterra systems
We investigate the existence, uniqueness and Gaussian curvature of the invariant carrying simplices of 3 species autonomous totally competitive Lotka-Volterra systems. Explicit examples are given where the carrying simplex is convex or concave, but also where the curvature is not single-signed. Our method monitors the curvature of an evolving surface that converges uniformly to the carrying sim...
متن کاملCarrying Simplices in Discrete Competitive Systems and Age-structured Semelparous Populations
For discrete competitive dynamical systems, amenable general conditions are presented to guarantee the existence of the carrying simplex and then these results are applied to age-structured semelparous population models, as well as to an annual plant competition model.
متن کاملSmoothness of Carrying Simplices for Three-dimensional Competitive Systems: a Counterexample
For a dissipative totally competitive system of ODEs ẋ = xf (x), ∂f /∂x < 0, i, j = 1, 2, 3, on the nonnegative octant K in R for which 0 is a repeller, M. W. Hirsch proved the existence of an invariant unordered Lipschitz surface (the carrying simplex) attracting all points in K \{0}. We give an example (of a Lotka–Volterra type) showing that the carrying simplex need not be of class C. AMS (M...
متن کاملExtinction in Nonautonomous Competitive Lotka-volterra Systems
It is well known that for the two species autonomous competitive Lotka-Volterra model with no fixed point in the open positive quadrant, one of the species is driven to extinction, whilst the other population stabilises at its own carrying capacity. In this paper we prove a generalisation of this result to nonautonomous systems of arbitrary finite dimension. That is, for the n species nonautono...
متن کاملOn the shadowing property of nonautonomous discrete systems
In this paper we study shadowing property for sequences of mappings on compact metric spaces, i.e. nonautonomous discrete dynamical systems. We investigate the relation of weak contractions with shadowing and h-shadowing property.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008