Stage-Structured Model of a Single-Species with Density-Dependent and Birth Pulses

摘要

A stage-structured mathematical model of a single-species with density-dependent birth pulses is proposed. We obtain exact periodic solutions of the system with birth pulses and threshold for stability of periodic solutions by studding the discrete dynamical system determined by the stroboscopic map. When the parameter of the system exceeds the threshold, there is a characteristic sequence of bifurcations, leading to chaos, growth law. The approach is based on the application of continuation theorem in Mawhin's coincidence degree theory