Global extinctions arising from Barnacle-Algae-Mussel interaction model

Abstract

In this article, based on the result of the uniform persistence for $ 4 $-dimensional autonomous system with interactions in a rocky intertidal community by Hsu et al.[7], the extinction of the model is further explored. According to the existence of the positive equilibrium, we rigorously classify three categories corresponding to extinct states of the three species Mussel, Algae and Barnacle, respectively. The extinction results of the $ 4 $-dimensional model in this paper exactly verify further the uniform persistence obtained in [7], and the classifications are total for the uniform persistence. What is rather more significant is that the distinguished criteria characterize the three extinct steady state. The global extinctions of the model are helpful to understand the mechanism of the the three species coexistence and the cyclic succession fluctuation observed in [1].