Oscillations and Coupling in Interconnections of Two-Dimensional Brain Networks

Oscillations in the brain are one of the most ubiquitous and robust patterns of activity and correlate with various cognitive phenomena. In this work, we study the existence and properties of oscillations in simple mean-field models of brain activity with bounded linear-threshold rate dynamics. First, we obtain exact conditions for the existence of limit cycles in two-dimensional excitatory-inhibitory networks (E-I pairs). Building on this result, we study networks of multiple E-I pairs, provide exact conditions for the lack of stable equilibria, and numerically show that this is a tight proxy for the existence of oscillatory behavior. Finally, we study cross-frequency coupling between pairs of oscillators each consisting of an E-I pair. We find that while both phase-phase coupling (synchronization) and phase-amplitude coupling (PAC) monotonically increase with inter-oscillator connection strength, there exists a tradeoff in increasing frequency mismatch between the oscillators as it desynchronizes them while enhancing their PAC.