Persistence and extinction threshold for homogeneous dynamical models with continuous time and its applications (Theory of Biomathematics and Its Applications XIV : Modelling and Analysis for Structured Population Dynamics and its Applications)

Abstract

In this paper, we develop a stability theory of the zero solution for the continuous-time homogeneous semilinear dynamical system. For the discrete-time homogeneous dynamical system, Thieme and Jin [6, 7, 8] show that the cone spectral radius of a homogeneous operator gives the threshold value for the stability of the zero solution. We apply this idea to the continuous-time dynamical system under appropriate conditions commonly used in population dynamics. Using this theory, we investigate a two-sex structured population model to find the threshold value for population extinction and persistence.