The balance simplex in non-competitive 2-species scaled Lotka–Volterra systems

Abstract

Explicit expressions in terms of Gaussian Hypergeometric functions are found for a ‘balance’ manifold that connects the non-zero steady states of a 2-species, non-competitive, scaled Lotka–Volterra system by the unique heteroclinic orbits. In this model, the parameters are the interspecific interaction coefficients which affects the form of the solution used. Similar to the carrying simplex of the competitive model, this balance simplex is the common boundary of the basin of repulsion of the origin and infinity, and is smooth except possibly at steady states.

Keywords

• balance simplex
• lotka–volterra
• carrying simplex
• gaussian hypergeometric function
• invariant manifold