منابع مشابه
On 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 کاملOn 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 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 کاملOn the Smoothness of Functors
In this paper we will try to introduce a good smoothness notion for a functor. We consider properties and conditions from geometry and algebraic geometry which we expect a smooth functor should has.
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...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-04887-x