Dynamic complexities in a single-species discrete population model with stage structure and birth pulses☆

Abstract

Abstract Natural population, whose population numbers are small and generations are non-overlapping, can be modelled by difference equations that describe how the population evolve in discrete time-steps. This paper investigates a recent study on the dynamics complexities in a single-species discrete population model with stage structure and birth pulses. Using the stroboscopic map, we obtain an exact cycle of system, and obtain the threshold conditions for its stability. Above this, there is a characteristic sequence of bifurcations, leading to chaotic dynamics, which implies that this the dynamical behaviors of the single-species discrete model with birth pulses are very complex, including (a) non-unique dynamics, meaning that several attractors and chaos coexist; (b) small-amplitude annual oscillations; (c) large-amplitude multi-annual cycles; (d) chaos. Some interesting results are obtained and they showed that pulsing provides a natural period or cyclicity that allows for a period-doubling route to chaos.