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Journal of Mathematical Biology

, Volume 44, Issue 2, pp 185–199 | Cite as

Density-dependent birth rate, birth pulses and their population dynamic consequences

  • Sanyi Tang
  • Lansun Chen
Article

Abstract.

 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. 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.

Keywords

Periodic Solution Bifurcation Diagram Chaotic Dynamic Impulsive Differential Equation Discrete Dynamical System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Sanyi Tang
    • 1
  • Lansun Chen
    • 1
  1. 1.Institute of Mathematics, Academy of Mathematics and System Sciences, Academia Sinica, Beijing 100080, P.R.China.CHINA

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