Modeling and Dynamic Analysis of Algae–Fish Model with Two State-Dependent Impulse Controls

In ecological modeling, symmetry can manifest in multiple ways, significantly contributing to our understanding of ecosystem stability, species interactions, and ecological balance. Considering the bloom phenomenon caused by excessive algae in ponds and its impact on aquaculture, we establish a class of algae–fish ecological models with two state-dependent impulse controls. In this paper, we first discuss the existence of positive equilibria in the system without impulses. Second, the existence and asymptotic stability of the order-1 and order-2 periodic solutions are analyzed by applying successor functions and a Similar Poincare Criterion. Finally, numerical simulations demonstrate that the model exhibits order-1 and order-2 periodic solutions, clarifying that the system with two impulses can address the problem more effectively.