Nonlinear semelparous leslie models.
Nonlinear semelparous leslie models.
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非线性半生莱斯利模型。
DOI：
10.3934/mbe.2006.3.17
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
J. Cushing
中科院分区：
文献类型：
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作者：
J. Cushing
本文考虑了一类结构种群动力学的一般非线性Leslie矩阵模型在平凡平衡点的分支，其中只有最古老的种群是可再生的。使用固有的净再生数n作为参数，我们证明了正平衡点的一个全局分支从n=1的平凡平衡点开始分支，尽管分支是非一般的。分支可以是超临界的，也可以是亚临界的，但与迭代模型中一般的跨临界分支不同，分支正平衡点的稳定性不是由分支的方向决定的。此外，我们还证明了单类循环的一个分支也从n=1的平凡平衡点分支出来。在两个种群类的情况下，分支平衡点或分支环是稳定的(但不是同时稳定的)，这取决于类间竞争和类内竞争的相对强度。激烈的阶级间竞争导致了两个种群阶级在时间上分离的稳定周期。在三类或更多类的情况下，分支环通常位于分支不变环上，该分支不变环的结构是由异宿轨道连接的周期循环的不同相位组成的循环链。在某些情况下，这些分支回路是吸引子。
In this paper we consider the bifurcations that occur at the trivial equilibrium of a general class of nonlinear Leslie matrix models for the dynamics of a structured population in which only the oldest class is reproductive. Using the inherent net reproductive number n as a parameter, we show that a global branch of positive equilibria bifurcates from the trivial equilibrium at n = 1 despite the fact that the bifurcation is nongeneric. The bifurcation can be either supercritical or subcritical, but unlike the case of a generic transcritical bifurcation in iteroparous models, the stability of the bifurcating positive equilibria is not determined by the direction of bifurcation. In addition we show that a branch of single-class cycles also bifurcates from the trivial equilibrium at n = 1. In the case of two population classes, either the bifurcating equilibria or the bifurcating cycles are stable (but not both) depending on the relative strengths of the inter- and intra-class competition. Strong inter-class competition leads to stable cycles in which the two population classes are temporally separated. In the case of three or more classes the bifurcating cycles often lie on a bifurcating invariant loop whose structure is that of a cycle chain consisting of the different phases of a periodic cycle connected by heteroclinic orbits. Under certain circumstances, these bifurcating loops are attractors.