In an ecosystem, species differ markedly in their ecological importance, rarity, and contributions to ecosystem stability. Effective ecosystem management requires prioritization strategies that account for these differences. This paper develops a weighted state-dependent impulsive control model for a predator-prey system incorporating anti-predator behavior. First, we analyze the existence and orbital asymptotic stability of the predator-extinction periodic solution. Using the harvesting rate $\sigma_{1}$ as a bifurcation parameter, we demonstrate that transcritical bifurcations occur near this solution through rigorous construction and analysis of a Poincaré map $P_{M}$ , revealing how strategic parameter adjustments can prevent predator extinction. Next, we derive threshold conditions for the existence and stability of positive order 1 periodic solutions by applying key properties of $P_{M}$ . The analysis is extended to higher-order periodic solutions ( $k = 2, 3$ ), establishing conditions under which complex population cycles emerge. Our results demonstrate that calibrated harvesting and predator-release parameters can maintain ecological balance while suppressing prey overabundance. Theoretical findings are validated through numerical simulations, which further illustrate the practical implications of parameter selection for long-term ecosystem sustainability.
