Coexistent steady-state solutions to a Lotka-Volterra model for two freely-dispersing competing species have been shown by several authors to arise as global secondary bifurcation phenomena. In this paper we establish conditions for the existence of global higher dimensional n-ary bifurcation in general systems of multiparameter nonlinear eigenvalue problems which preserve the coupling structure of diffusive steady-state Lotka-Volterra models. In establishing our result, we mainly employ the recently-developed multidimensional global multiparameter theory of Alexander-Antman. Conditions for ternary steady-state bifurcation in the three species diffusive competition model are given as an application of the result.
|Original language||English (US)|
|Number of pages||8|
|Journal||Proceedings of the Royal Society of Edinburgh Section A: Mathematics|
|State||Published - 1987|
ASJC Scopus subject areas