  The guiding centre dynamics of fast particles can alter the behaviour of
energetic particle driven modes with chirping frequencies. In this paper, the
applicability of an earlier trapped/passing locus model [H. Hezaveh et al 2017
Nucl. Fusion 57 126010] has been extended to regimes where the wave trapping
region can expand and trap ambient particles. This extension allows the study
of waves with up-ward and down-ward frequency chirping across the full range of
energetic particle orbits. Under the adiabatic approximation, the phase-space
of energetic particles is analysed by a Lagrangian contour approach where the
islands are discretised using phase-space waterbags. In order to resolve the
dynamics during the fast formation of phase-space islands and find an
appropriate initialisation for the system, full-scale modelling is implemented
using the bump-on-tail (BOT) code. In addition to investigating the evolution
of chirping waves with deepening potentials in a single resonance, we choose
specific pitch-angle ranges in which higher resonances can have a relatively
considerable contribution to the wave-particle interaction. Hence, the model is
also solved in a double-resonance scenario where we report on the significant
modifications to the behaviour of the chirping waves due to the $2^{\text{nd}}$
resonance. The model presented in this paper gives a comprehensive 1D paradigm
of long range frequency chirping signals observed in experiments with both
up-ward and down-ward chirping and multiple resonances.
