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首页> 外文期刊>International Journal of Innovative Computing Information and Control >ON THE BIFURCATION BEHAVIOR OF A THREE-SPECIES LOTKA-VOLTERRA FOOD CHAIN MODEL WITH TWO DISCRETE DELAYS
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ON THE BIFURCATION BEHAVIOR OF A THREE-SPECIES LOTKA-VOLTERRA FOOD CHAIN MODEL WITH TWO DISCRETE DELAYS

机译:两种时滞的三种种群洛卡-沃尔特拉食物链模型的分叉行为

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摘要

In this paper, a three-species Lotka- Volterra food chain model with two discrete delays is investigated, where the time delays are regarded as parameters. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic transcendental equation, it is found that Hopf bifurcation occurs when these delays pass through a sequence of critical value. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions are derived by using the normal form theory and center manifold theory. Finally, numerical simulations supporting the theoretical analysis are carried out.
机译:本文研究了具有两个离散延迟的三种群Lotka-Volterra食物链模型,其中将时间延迟作为参数。根据局部分析和Hopf分叉分析研究了其动力学。通过分析相关的特征先验方程,发现当这些延迟通过一系列临界值时,发生霍普夫分叉。利用范式理论和中心流形理论推导了确定Hopf分支周期解的稳定性和方向的一些明确公式。最后,进行了支持理论分析的数值模拟。

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