Optimizing impulsive releases : a species competition model

Abstract

This study focuses on optimizing species release S2 to control species population S1 through impulsive release strategies. We investigate the conditions required to remove species S1, which is equivalent to the establishment of S2. 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 S1 - free solution. In addition, we formulate an optimal control problem to maximize the effectiveness of S2 releases, manage the population of S1, 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.