We propose and analyze a stochastic competing two-species population dynamics model subject to jump and continuous correlated noises. Competing benthic algae population dynamics in river environment, which is an important engineering problem, motivates this new model. The model is a system of stochastic differential equations having a characteristic that the two populations are competing with each other through the environmental capacities; an increase in one population decreases the other’s environmental capacity. Unique existence of the uniformly bounded strong solution is proven, and attractors of the solutions are identified depending on the parameter values. The Kolmogorov’s backward equation associated with the population dynamics is formulated and its unique solvability in a Banach space with a weighted norm is discussed. A novel uncertain correlation case is also analyzed in the framework of viscosity solutions. Numerical computation results using a finite difference scheme and a Monte-Carlo method are presented to deeper analyze the model. Our analysis results can be utilized for establishment of a foundation for modeling, analysis and control of the competing population dynamics.

中文翻译：

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两种物种在随机干扰下竞争种群动态与种群依赖的环境容量。

我们提出并分析了受跳跃和连续相关噪声影响的随机竞争的两个物种种群动态模型。河流环境中竞争底栖藻类种群动态是一个重要的工程问题，激发了这种新模型。该模型是一个随机微分方程组，其特征是两个种群通过环境容量相互竞争；一个人口的增加会降低另一个的环境容量。证明了一致有界强解的唯一存在性，并根据参数值确定解的吸引子。公式化了与种群动态相关的 Kolmogorov 后向方程，并讨论了它在具有加权范数的 Banach 空间中的独特可解性。还在粘度解的框架内分析了一种新的不确定相关性情况。使用有限差分方案和蒙特卡罗方法的数值计算结果被提出以更深入地分析模型。我们的分析结果可用于为竞争性种群动态的建模、分析和控制奠定基础。