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Zbl 0990.92033
Tang, Sanyi; Chen, Lansun
Density-dependent birth rate, birth pulses and their population dynamic consequences. (English)
[J] J. Math. Biol. 44, No.2, 185-199 (2002). ISSN 0303-6812; ISSN 1432-1416/e

Summary: In most models of population dynamics, increases in population due to birth are assumed to be time-independent, but many species reproduce only during a single period of the year. We propose a single-species model with stage structure for the dynamics in a wild animal population for which births occur in a single pulse once per time period. Using the discrete dynamical system determined by the stroboscopic map, we obtain an exact periodic solution of systems which are with Ricker functions or Beverton-Holt functions, and obtain the threshold conditions for their stability.\par Above this threshold, there is a characteristic sequence of bifurcations, leading to chaotic dynamics, which implies that the dynamical behaviors of the single species model with birth pulses are very complex, including small-amplitude annual oscillations, large-amplitude multi-annual cycles, and chaos. This suggests that birth pulse, in effect, provides a natural period or cyclicity that allows for a period-doubling route to chaos.

MSC 2000:: *92D25 Population dynamics
37N25 Dynamical systems in biology
37D45 Strange attractors, chaotic dynamics

Keywords: density dependence; birth pulses; stage structure

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