Stochastic Lotka-Volterra competitive reaction-diffusion systems perturbed by space-time white noise: Modeling and analysis
Stochastic Lotka-Volterra competitive reaction-diffusion systems perturbed by space-time white noise: Modeling and analysis
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DOI：
10.1016/j.jde.2021.02.023
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发表时间：
2020-12
影响因子：
2.4
通讯作者：
N. Nguyen;G. Yin
中科院分区：
文献类型：
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作者：
N. Nguyen;G. Yin
受传统Lotka-Volterra竞争模型的启发，本文提出并分析了一类随机反应扩散偏微分方程。与文献中的模型相比，新的配方使物种的空间依赖性。此外，噪声过程允许是时空白色噪声。本文研究了具有非Lipschitz和非线性增长系数及乘性噪声的随机反应扩散方程组的适定性、解的正则性、密度的存在性和不变测度的存在性.结合随机场方法和SPDE中的无穷积分理论方法对弱解进行了分析。在此基础上，本文建立了一般情形下的Lotka-Volterra竞争系统，并利用随机微积分中的新工具研究了该系统的长期性质。
Motivated by the traditional Lotka-Volterra competitive models, this paper proposes and analyzes a class of stochastic reaction-diffusion partial differential equations. In contrast to the models in the literature, the new formulation enables spatial dependence of the species. In addition, the noise process is allowed to be space-time white noise. In this work, well-posedness, regularity of solutions, existence of density, and existence of an invariant measure for stochastic reaction-diffusion systems with non-Lipschitz and non-linear growth coefficients and multiplicative noise are considered. By combining the random field approach and infinite integration theory approach in SPDEs for mild solutions, analysis is carried out. Then this paper develops a Lotka-Volterra competitive system under general setting; longtime properties are studied with the help of newly developed tools in stochastic calculus.