On existence and uniqueness of the carrying simplex for competitive dynamical systems

TL;DR

This paper investigates the conditions under which competitive dynamical systems possess a unique invariant hypersurface, called the carrying simplex, to which all nonzero trajectories asymptotically converge, highlighting its geometric and topological properties.

Contribution

It establishes the existence and uniqueness of the carrying simplex in certain competitive dynamical systems, providing a rigorous mathematical foundation.

Findings

Existence of a unique invariant hypersurface in competitive systems

Trajectories asymptotically approach the carrying simplex

The carrying simplex has simple geometry and topology

Abstract

Certain dynamical models of competition have a unique invariant hypersurface to whichevery nonzero tractory is asymptotic, having simple geometry and topology.