Stochastic Bifurcation in the Plankton System under the Fish School
Stochastic Bifurcation in the Plankton System under the Fish School
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DOI：
10.5687/sss.2015.225
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发表时间：
2015-05
期刊：
影响因子：
--
通讯作者：
M. Ishikawa
中科院分区：
文献类型：
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作者：
M. Ishikawa
由于每种生物都通过食物链相互作用，因此对食物链的分析是生态系统中的一个关键问题。本文研究了由鱼、浮游动物和浮游植物组成的浮游生物-鱼系统，通过数值模拟研究了随机噪声对鱼群浮游生物系统稳定性的影响。微分方程解因系统参数的变化而发生质的变化，通常称为分叉。本文研究了一类随机浮游生物-鱼系统的分叉问题。作为随机分叉的主要分析方法，P分叉(唯象分叉)和D分叉(动态分叉)方法被引用。P-分支研究与单点运动对应的平稳测度，而D-分支则考虑不变测度的稳定性。由于P-分岔法是基于一点运动的，因此有可能遗漏分岔图中的某些分支。因此，我们利用D-分叉来研究随机浮游生物-鱼类系统的分叉。数值模拟结果表明，本文所研究的随机浮游生物-鱼类系统不存在D-分叉现象。
Since each creature interacts with each other through a food chain, an analysis of the food chain is a crucial problem in an ecosystem. In this paper, we consider the plankton-fish system consisting of fish, zooplankton and phytoplankton, and study the influence of the random noise on the stability of the plankton system under fish school by numerical simulations. The qualitative change of the solutions of differential equations by variation of a system parameter is generally called a bifurcation. This paper is concerned with the bifurcation analysis of a stochastic plankton-fish system. As major analytical methods for the stochastic bifurcation, the P-bifurcation (Phenomenological bifurcation) and the D-bifurcation (Dynamical bifurcation) approaches are cited. The P-bifurcation studies a stationary measure corresponding to the one-point motion, while the D-bifurcation considers the stability of invariant measures. Since the P-bifurcation approach is based on the one point-motion, there is a possibility to miss certain branches in bifurcation diagrams. So, we study the bifurcation in the stochastic plankton-fish system using the D-bifurcation. By the numerical simulations, we show that the D-bifurcation does not occur in the stochastic plankton-fish system considered here.