<p>In recent years, bursting dynamics in nonlinear systems under amplitude modulation have attracted significant attention from researchers. Unlike the previous study on the Mathieu-van der Pol-Duffing system that considered a 2:1 ratio of excitation frequency to modulation frequency, this paper investigates the bursting dynamics under a 1:1 ratio condition. We find that the amplitude-modulated system studied here is jointly governed by two sub-vector fields, demonstrating a notable distinction from the previous studies involving one single vector field systems. As a result, interesting bursting dynamics, especially delayed pitchfork bursting oscillations of “point-cycle” type with variable large amplitude, can be obtained. By employing the frequency-transformation fast-slow method, we reveal dynamical mechanisms of the bursting oscillations with variable large amplitude. Our study shows that amplitude modulation critically governs stability conditions and bifurcation structures in the fast subsystems. Specifically, this modulation can trigger additional bifurcation phenomena and alter the pitchfork bifurcation delay, which further leads to the system’s ability to transition between/among periodic orbits with different amplitudes, thereby forming bursting oscillations with variable large amplitude. The study reveals the significant impact of amplitude modulation on bursting dynamics, providing important references for analyzing amplitude-modulated bursting phenomena involving delayed pitchfork bifurcations in broader nonlinear contexts.</p>