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Propagation of Stochastic Travelling Waves of Cooperative Systems with Noise

Discrete and Continuous Dynamical Systems - Series B(2022)

Natl Univ Def Technol

Cited 3|Views1
Abstract
We consider the cooperative system driven by a multiplicative It\^o type white noise. The existence and their approximations of the travelling wave solutions are proven. With a moderately strong noise, the travelling wave solutions are constricted by choosing a suitable marker of wavefront. Moreover, the stochastic Feynman-Kac formula, sup-solution, sub-solution and equilibrium points of the dynamical system corresponding to the stochastic cooperative system are utilized to estimate the asymptotic wave speed, which is closely related to the white noise.
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Stochastic competition-cooperation system,travelling wave solution,upper/lower solution,asymptotic wave speed,Feynman-Kac formula
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要点】:本文研究了受乘性伊藤型白噪声驱动的合作系统的随机行波解的存在性和近似,并利用随机Feynman-Kac公式等方法估计了与白噪声紧密相关的渐进波速。

方法】:通过选择合适的波前标记,利用随机Feynman-Kac公式、上解、下解以及对应于随机合作系统的动力系统的平衡点来证明行波解的存在并估计其速度。

实验】:论文未明确描述具体实验过程和数据集,重点在于理论分析和数学证明,得出在适度强噪声下,行波解受限于波前标记的选择,且渐进波速与白噪声有关。