Tang Sanyi, Chen Lansun
Institute of Mathematics, Academy of Mathematics and System Sciences, Academia Sinica, Beijing, PR China.
J Math Biol. 2002 Feb;44(2):185-99. doi: 10.1007/s002850100121.
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.
在大多数种群动态模型中，因出生导致的种群增长被假定为与时间无关，但许多物种只在一年中的单一时期繁殖。我们针对一个野生动物种群的动态提出了一个具有阶段结构的单物种模型，其中出生在每个时间段以单个脉冲的形式发生一次。利用频闪映射确定的离散动力系统，我们得到了具有里克函数或贝弗顿 - 霍尔特函数的系统的精确周期解，并获得了其稳定性的阈值条件。高于此阈值，存在一系列特征性的分岔，导致混沌动力学，这意味着具有出生脉冲的单物种模型的动态行为非常复杂，包括小幅度的年度振荡、大幅度的多年周期以及混沌。这表明出生脉冲实际上提供了一个自然周期或周期性，使得通向混沌的倍周期途径成为可能。
