Stability Analysis of a Population Model with Maturation Delay and Ricker Birth Function
Stability Analysis of a Population Model with Maturation Delay and Ricker Birth Function
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具有成熟延迟和Ricker出生函数的种群模型的稳定性分析
DOI：
10.1155/2014/136707
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发表时间：
2014
影响因子：
--
通讯作者：
Li Jianquan
中科院分区：
文献类型：
--
作者：
Zheng Chongwu;Zhang Fengqin;Li Jianquan
研究了一类具有离散成熟时滞和Ricker出生函数的单种群模型。得到了判定平凡平衡点全局稳定性和正平衡点存在性的阈值。利用Pontryagin方法给出了正平衡点局部渐近稳定的充分必要条件。分析了各参数取值对正平衡点局部稳定性的影响。所得结果表明了稳定切换的存在，并提供了一种计算稳定切换发生时的成熟时间的方法。数值模拟表明，该模型可能发生混沌，并给出了相应的参数分岔图的某些值。
A single species population model is investigated, where the discrete maturation delay and the Ricker birth function are incorporated. The threshold determining the global stability of the trivial equilibrium and the existence of the positive equilibrium is obtained. The necessary and sufficient conditions ensuring the local asymptotical stability of the positive equilibrium are given by applying the Pontryagin′s method. The effect of all the parameter values on the local stability of the positive equilibrium is analyzed. The obtained results show the existence of stability switch and provide a method of computing maturation times at which the stability switch occurs. Numerical simulations illustrate that chaos may occur for the model, and the associated parameter bifurcation diagrams are given for certain values of the parameters.