[MS10] Model Bifurcations and Ecological Relevance

[MS10-09] Discrete-time resident-invader dynamics

*Ryusuke Kon¹ (1. University of Miyazaki (Japan))

Keywords:

resident-invader dynamics,discrete-time models,difference equations,two-species competition models

We study a certain class of the discrete-time resident-invader dynamics and extend two theorems, which have been established already for the continuous-time resident-invader dynamics by Geritz (2005). The proof relies on the result on the existence of the invariant curve connecting two axial fixed points (Kon, 2003). The two theorems assume that the resident and invader strategies are similar to one another. The first theorem shows that in a neighborhood of a non-singular strategy invasion implies fixation of the invader. The second theorem classifies the global dynamics on the invariant curve connecting two axial fixed points in terms of the invasin conditions.