霍普夫分叉
白噪声
数学
噪音(视频)
随机微分方程
统计物理学
平稳分布
分叉
人口
数学分析
应用数学
物理
非线性系统
统计
马尔可夫链
量子力学
图像(数学)
社会学
人口学
人工智能
计算机科学
作者
Susmita Sadhu,Christian Kuehn
出处
期刊:Chaos
[American Institute of Physics]
日期:2018-03-01
卷期号:28 (3)
被引量:18
摘要
The effect of demographic stochasticity, in the form of Gaussian white noise, in a predator-prey model with one fast and two slow variables is studied. We derive the stochastic differential equations (SDEs) from a discrete model. For suitable parameter values, the deterministic drift part of the model admits a folded node singularity and exhibits a singular Hopf bifurcation. We focus on the parameter regime near the Hopf bifurcation, where small amplitude oscillations exist as stable dynamics in the absence of noise. In this regime, the stochastic model admits noise-driven mixed-mode oscillations (MMOs), which capture the intermediate dynamics between two cycles of population outbreaks. We perform numerical simulations to calculate the distribution of the random number of small oscillations between successive spikes for varying noise intensities and distance to the Hopf bifurcation. We also study the effect of noise on a suitable Poincaré map. Finally, we prove that the stochastic model can be transformed into a normal form near the folded node, which can be linked to recent results on the interplay between deterministic and stochastic small amplitude oscillations. The normal form can also be used to study the parameter influence on the noise level near folded singularities.
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