考虑不同类型响应函数的浮游生物群落简单数学模型的动态比较分析

Q3 Mathematics
G. P. Neverova, O. Zhdanova
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引用次数: 0

摘要

考虑浮游植物和浮游动物的发育和相互作用的特点,提出了浮游生物群落的双组分离散时间模型。为了描述这些物种之间的相互作用并比较系统动力学,我们使用了以下响应函数:II型和III型Holling函数和Arditi-Ginzburg响应函数,每个响应函数都描述了浮游植物和浮游动物之间的营养相互作用。对所提出的模型进行了分析和数值研究。分析表明,营养函数的变化不会从根本上改变模型的动力行为。根据neimmark - saker情景,与浮游植物和浮游动物共存相对应的非重要不动点的稳定性损失可以通过一系列倍周期分岔发生,这使我们能够观察到长周期振荡的出现,这些振荡代表了捕食者-猎物相互作用导致的峰值交替和物种数量减少。同时,该模型具有多稳定区,在初始条件发生变化且所有模型参数值不变的情况下,会导致当前动态模式发生移位。当当前社区结构的变化可能导致整个社区或其部分社区的灭绝时,每个模型都显示出条件共存。考虑到物种组成的特点,具有II型Holling函数的模型似乎更适合描述浮游生物群落的动态。这种系统与浮游植物是快速变化的,而捕食者的动态是缓慢的观点是一致的;因此,长周期波动发生在浮游植物生长速率高和浮游动物生长速率低的地方。具有Arditi-Ginzburg函数响应的模型在高捕食者生长率和低猎物生长率的窄参数区表现出准周期波动。模型中具有Holling III型功能响应的准周期动力学区域对应于快变量和慢变量的概念,但在这种情况下,系统的稳定性增加,即使在较高的浮游动物生长速率下也会发生neimmark - sacker分岔。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Comparative Dynamics Analysis of Simple Mathematical Models of the Plankton Communities Considering Various Types of Response Function
The paper proposes a two-component discrete-time model of the plankton community, taking into account features of the development and interaction of phytoplankton and zooplankton. To describe the interaction between these species and to compare the system dynamics, we use the following set of response functions: type II and III Holling function and the Arditi–Ginzburg response function, each of which describes trophic interactions between phytoplankton and zooplankton. An analytical and numerical study of the model proposed is made. The analysis shows that the variation of trophic functions does not change the dynamic behavior of the model fundamentally. The stability loss of nontrivial fixed point corresponding to the coexistence of phytoplankton and zooplankton can occur through a cascade of period-doubling bifurcations and according to the Neimark–Saker scenario, which allows us to observe the appearance of long-period oscillations representing the alternation of peaks and reduction in the number of species as a result of the predator-prey interaction. As well, the model has multistability areas, where a variation in initial conditions with the unchanged values of all model parameters can result in a shift of the current dynamic mode. Each of the models is shown to demonstrate conditional coexistence when a variation of the current community structure can lead to the extinction of the entire community or its part. Considering the characteristics of the species composition, the model with the type II Holling function seems a more suitable for describing the dynamics of the plankton community. Such a system is consistent with the idea that phytoplankton is a fast variable and predator dynamics is slow; thus, long-period fluctuations occur at high phytoplankton growth rates and low zooplankton ones. The model with the Arditi–Ginzburg functional response demonstrates quasi-periodic fluctuations in a narrow parametric aria with a high predator growth rate and low prey growth rate. The quasi-periodic dynamics regions in the model with the Holling type III functional response correspond to the conception of fast and slow variables, however in this case, the stability of the system increases, and the Neimark-Sacker bifurcation occurs even at a higher growth rate of zooplankton.
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来源期刊
Mathematical Biology and Bioinformatics
Mathematical Biology and Bioinformatics Mathematics-Applied Mathematics
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1.10
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