Aiming at the problems of random disturbances, unknown nonlinear terms, and control resource consumption in biological systems invaded by alien species, the present study proposes a control strategy that fuses the Generalized Fuzzy Hyperbolic Model (GFHM) with the event-triggered mechanism. First, the GFHM is employed to substitute for the conventional Fuzzy Logic System (FLS) in approximating the system’s unknown nonlinear terms, and its structural advantage based on hyperbolic tangent functions is utilized to improve approximation accuracy. Secondly, an appropriate controller is designed via the backstepping method. In order to cut down on superfluous control signal transmission and decrease communication costs, an event-triggered mechanism is incorporated into the controller design, while the actual control input is updated discretely only when the predefined error threshold is surpassed. Theoretical investigations demonstrate that the proposed strategy can guarantee all system states maintain semi-global uniform ultimate boundedness, while the tracking error of native species density converges toward a small neighborhood around zero. In simulation experiments, the invasion of Hypostomus plecostomus is taken as an example, and the superiority of the proposed method in control accuracy is verified.