Title: Controllability of diffusive Lotka-Volterra strongly competitive systems under boundary constrained controls Show Chinese title

Title: 具有边界约束控制的扩散Lotka-Volterra强竞争系统的能控性

Abstract: We investigate the controllability of the competition-diffusion Lotka-Volterra system. Our primary focus is on the one-dimensional setting with Dirichlet boundary controls, interpreted as ecological management policies regulating the density of species at the habitat boundaries and satisfying bilateral constraints. We show that the system can be steered from any initial state to a constant steady state representing the extinction of the less competitive species. In contrast, we prove that controllability toward a steady state where the more competitive species vanishes is generally not achievable when the inter-species competition rates are too unbalanced. This obstruction is due to the existence of barrier solutions, which we explicitly construct based on the spectral properties of the associated reaction-diffusion operators. Our theoretical results are illustrated through numerical simulations and are accompanied by a discussion of open problems and potential directions for future research. Show Chinese abstract

Abstract: 我们研究竞争扩散Lotka-Volterra系统的可控性。 我们的主要关注点是一维情况下的Dirichlet边界控制，被解释为生态管理政策，调节栖息地边界处物种的密度并满足双边约束。 我们证明，系统可以从任何初始状态被引导到一个表示较不具竞争力物种灭绝的常数稳态。 相反，我们证明当种间竞争率过于不平衡时，通常无法实现向一个更具有竞争力物种消失的稳态的可控性。 这种障碍是由于存在障碍解，我们根据相关反应扩散算子的谱特性显式构造了这些障碍解。 我们的理论结果通过数值模拟进行了说明，并附有对开放问题和未来研究潜在方向的讨论。