Dynamic complexities in a single-species discrete population model with stage structure and birth pulses. (English) Zbl 1066.92041

Gao, Shujing; Chen, Lansun

Chaos Solitons Fractals 23, No. 2, 519-527 (2005).

Summary: Natural populations, whose population numbers are small and generations non-overlapping, can be modelled by difference equations that describe how the populations evolve in discrete time-steps. This paper investigates a recent study on the dynamic complexities in a single-species discrete population model with stage structure and birth pulses. Using the stroboscopic map, we obtain an exact cycle of the system, and obtain a threshold conditions for its stability. Above this, there is a characteristic sequence of bifurcations, leading to chaotic dynamics, which implies that 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.

MSC:

92D25	Population dynamics (general)
37N25	Dynamical systems in biology
37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior

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