منابع مشابه
On peaks in carrying simplices
A necessary and sufficient condition is given for the carrying simplex of a dissipative totally competitive system of three ordinary differential equations to have a peak singularity at an axial equilibrium. For systems of Lotka–Volterra type that result translates into a simple condition on the coefficients.
متن کاملOn Smoothness of Carrying Simplices
We consider dissipative strongly competitive systems ẋi = xifi(x) of ordinary differential equations. It is known that for a wide class of such systems there exists an invariant attracting hypersurface Σ, called the carrying simplex. In this note we give an amenable condition for Σ to be a C1 submanifold-with-corners. We also provide conditions, based on a recent work of M. Benäım (On invariant...
متن کاملCarrying simplices in nonautonomous and random competitive Kolmogorov systems
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 El...
متن کاملOn Minkowski sums of simplices
We investigate the structure of the Minkowski sum of standard simplices in R. In particular, we investigate the one-dimensional structure, the vertices, their degrees and the edges in the Minkowski sum polytope. 2000 MSC: 52B05, 52B11, 05C07.
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.
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1999
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-81-2-285-292