Dynamics of bicomponent phase oscillators model with nearest-neighbor and next-nearest-neighbor interactions: Impact of heterogeneity and dynamical transitions

We investigate the dynamics of a bicomponent phase oscillators model with nearest-neighbor and next-nearest-neighbor interactions, where two distinct types of oscillators with different coupling strengths are introduced. We focus on how the presence of minority oscillators affects the collective dynamics and how the system evolves as the proportion p of type-A oscillators changes. We find that a small fraction of type-A oscillators can significantly perturb the system, disrupting the uniform order of the predominantly type-B oscillators and inducing complex local excitations, including periodic and chaotic-like fluctuations. As p varies from 0 to 1, the system exhibits a range of dynamical transitions, including continuous crossovers between in-phase and anti-phase orders, as well as more complex behaviors involving bimodal and uniform distributions of phase differences. Our findings emphasize that the spatial distribution and prevalence of local excitations are intricately controlled by the alignment of coupling parameters. This work provides a deeper understanding of how heterogeneity in coupling strengths influences the collective behavior of coupled oscillator systems.