Ural Federal University, Ekaterinburg, Russian Federation.
University of Hohenheim, Stuttgart, Germany.
Philos Trans A Math Phys Eng Sci. 2020 May 15;378(2171):20190253. doi: 10.1098/rsta.2019.0253. Epub 2020 Apr 13.
We study the effects of noise and diffusion in an excitable slow-fast population system of the Leslie-Gower type. The phenomenon of noise-induced excitement is investigated in the zone of stable equilibria near the Andronov-Hopf bifurcation with the Canard explosion. The stochastic generation of mixed-mode oscillations is studied by numerical simulation and stochastic sensitivity analysis. Effects of the diffusion are considered for the spatially distributed variant of this slow-fast population model. The phenomenon of the diffusion-induced generation of spatial patterns-attractors in the Turing instability zone is demonstrated. The multistability and variety of transient processes of the pattern formation are discussed. This article is part of the theme issue 'Patterns in soft and biological matters'.
我们研究了噪声和扩散对兴奋型快慢种群 Leslie-Gower 系统的影响。在具有卡纳德爆炸的 Andronov-Hopf 分岔附近的稳定平衡点区域中，研究了噪声诱导兴奋的现象。通过数值模拟和随机灵敏度分析研究了随机混合模式振荡的产生。考虑了该快慢种群模型的空间分布变体的扩散效应。展示了在 Turing 不稳定性区域中扩散诱导空间模式吸引子产生的现象。讨论了模式形成的瞬态过程的多稳定性和多样性。本文是“软物质和生物物质中的模式”主题特刊的一部分。
