A novel 2D nonlinear dynamical paradigm is constructed to interpret the fast and repetitive frequency chirping and amplitude oscillation of Alfvén eigenmodes excited by energetic particles in fusion plasmas as observed in global gyrokinetic simulations. In this non-perturbative paradigm of the collisionless phase-space dynamics, wave-particle resonant interactions cause the phase-space structure to continuously twist and fold, leading to the repetitive excitation and decay of the Alfvén eigenmode. The radial (perpendicular to the dominant wave-particle interaction) dependence of the mode amplitude and toroidal precessional drifts of the energetic particles leads to the 2D dynamics of wave-particle interactions, which is found to be responsible for the repetitive process of formation and destruction of the mode structure.