本文研究了具有布朗运动的污染物对河流种群影响的时空模型的长期行为。首先在传统控制策略的基础上,创新性地引入了随机扰动,提出了一种新型的适应性控制策略,以应对环境变化带来的不确定性。证明了该模型具有全局正解和平稳分布的存...本文研究了具有布朗运动的污染物对河流种群影响的时空模型的长期行为。首先在传统控制策略的基础上,创新性地引入了随机扰动,提出了一种新型的适应性控制策略,以应对环境变化带来的不确定性。证明了该模型具有全局正解和平稳分布的存在唯一性,确保了模型的理论基础,为后续分析奠定基础。然后,考虑到污染物对河流种群的影响,将河流种群扩散模型引入控制策略,利用庞特里亚金的随机极大值原理,得到了随机河流种群扩散模型的近优性控制的充要条件。This paper studies the long-term behavior of a spatiotemporal model concerning the impact of pollutants with Brownian motion on river populations. First, based on traditional control strategies, we innovatively introduce stochastic perturbations and propose a novel adaptive control strategy to address the uncertainties brought about by environmental changes. We prove the existence and uniqueness of global positive solutions and stationary distributions for the model, ensuring its theoretical foundation and laying the groundwork for subsequent analyses. Next, considering the impact of pollutants on river populations, we incorporate the river population diffusion model into control strategies and, using Pontryagin’s stochastic maximum principle, derive the necessary and sufficient conditions for near-optimal control of the stochastic river population diffusion model.展开更多
文摘本文研究了具有布朗运动的污染物对河流种群影响的时空模型的长期行为。首先在传统控制策略的基础上,创新性地引入了随机扰动,提出了一种新型的适应性控制策略,以应对环境变化带来的不确定性。证明了该模型具有全局正解和平稳分布的存在唯一性,确保了模型的理论基础,为后续分析奠定基础。然后,考虑到污染物对河流种群的影响,将河流种群扩散模型引入控制策略,利用庞特里亚金的随机极大值原理,得到了随机河流种群扩散模型的近优性控制的充要条件。This paper studies the long-term behavior of a spatiotemporal model concerning the impact of pollutants with Brownian motion on river populations. First, based on traditional control strategies, we innovatively introduce stochastic perturbations and propose a novel adaptive control strategy to address the uncertainties brought about by environmental changes. We prove the existence and uniqueness of global positive solutions and stationary distributions for the model, ensuring its theoretical foundation and laying the groundwork for subsequent analyses. Next, considering the impact of pollutants on river populations, we incorporate the river population diffusion model into control strategies and, using Pontryagin’s stochastic maximum principle, derive the necessary and sufficient conditions for near-optimal control of the stochastic river population diffusion model.
