Chaotic dynamics of a nonlinear density dependent population model
Chaotic dynamics of a nonlinear density dependent population model
复制标题
非线性密度相关总体模型的混沌动力学
DOI：
10.1088/0951-7715/17/5/007
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发表时间：
2004
期刊：
影响因子：
1.7
通讯作者：
H. Weiss
中科院分区：
文献类型：
--
作者：
Ilie Ugarcovici;H. Weiss
我们研究过度补偿莱斯利人口模型的动态，其中生育率随着人口规模呈指数下降。我们发现了大量复杂的动力学行为，其中一些以前没有在种群模型中观察到，这可能会在种群生物学和人口学中产生新的范式。我们研究了二维和三维模型，发现了各种各样的复杂行为：所有余维1局部分岔，倍周期级联，吸引分叉成奇怪吸引子的闭合曲线，具有大盆地的多个共存奇怪吸引子（这导致 内在缺乏“遍历性”），可能导致不连续的大规模人口波动、吸引子合并、锁相和短暂混乱的危机。我们发现（并解释）两个不同的分叉级联将吸引不变的闭合曲线转变为奇怪的吸引子。我们还发现单参数族表现出大多数这些现象。我们表明，一些更奇特的现象是由同宿切线引起的。
We study the dynamics of an overcompensatory Leslie population model where the fertility rates decay exponentially with population size. We find a plethora of complicated dynamical behaviour, some of which has not been previously observed in population models and which may give rise to new paradigms in population biology and demography.We study the two- and three-dimensional models and find a large variety of complicated behaviour: all codimension 1 local bifurcations, period doubling cascades, attracting closed curves that bifurcate into strange attractors, multiple coexisting strange attractors with large basins (which cause an intrinsic lack of 'ergodicity'), crises that can cause a discontinuous large population swing, merging of attractors, phase locking and transient chaos. We find (and explain) two different bifurcation cascades transforming an attracting invariant closed curve into a strange attractor. We also find one-parameter families that exhibit most of these phenomena. We show that some of the more exotic phenomena arise from homoclinic tangencies.