Phase-amplitude coupling in neuronal oscillator networks

Cross-frequency phase-amplitude coupling (PAC) describes the phenomenon where the power of a highfrequency oscillation evolves with the phase of a low-frequency one. It has been widely observed in the brain and linked to various brain functions. In this paper, we show that Stuart-Landau oscillators coupled in a nonlinear fashion can give rise to PAC in two commonly accepted architectures, namely, (1) a high-frequency neural oscillation driven by an external low-frequency input and (2) two interacting local oscillations with distinct, locally generated frequencies. We characterize the parameters that affect PAC behavior, thus providing insight on this phenomenon observed in neuronal networks. Inspired by some empirical studies, we further present an interconnection structure for brain regions wherein cross-region interactions are established only by lowfrequency oscillations. We then demonstrate that low-frequency phase synchrony can integrate high-frequency activities regulated by local PAC and control the direction of information flow between distant regions.