Optimizing Impulsive Releases: A Species Competition Model

Abstract

This study focuses on optimizing species release $S_2$ to control species population $S_1$ through impulsive release strategies. We investigate the conditions required to remove species $S_1$, which is equivalent to the establishment of $S_2$. The research includes a theoretical analysis that examines the positivity, existence, and uniqueness of solutions, the conditions ensuring global stability, and a sufficient condition for controlling the $S_1$-free solution. In addition, we formulate an optimal control problem to maximize the effectiveness of $S_2$ releases, manage the population of $S_1$, and minimize the costs associated with this intervention strategy. Numerical simulations are conducted to validate the proposed theories and allow visualization of population dynamics under various release scenarios.

22 pages, 16 figures