Study competition models with constant harvest and state feedback control, and analyze population dynamics in fisheries and animal husbandry. Establish a mathematical model, analyze the existence and stability of equilibrium points, and apply Dulac discriminant method and Poincare criterion to study periodic solutions. Discovered the existence of stable nodes or focal points in the system under specific conditions, and proved the asymptotic stability of first-order periodic solutions. Reasonable control of harvest rates and feedback mechanisms can achieve sustainable population management, providing theoretical guidance for fisheries and animal husbandry.