Dynamics of multiple interacting excitatory and inhibitory populations with delays

A network consisting of excitatory and inhibitory (EI) neurons is a canonical model for understanding cortical network activity. In this study, we extend the EI network model and investigate how its dynamical landscape can be enriched when it interacts with another excitatory (E) population with transmission delays. Through analysis and simulations of a rate model and a spiking network model, we study the transition from stationary to oscillatory states by analyzing the Hopf bifurcation structure in terms of two network parameters: 1) transmission delay between the EI subnetwork and the E population and 2) inhibitory couplings that induce oscillatory activity in the EI subnetwork. We find that the critical coupling strength can strongly modulate as a function of transmission delay, and consequently the stationary state is interwoven intricately with oscillatory states generating different frequency modes. This leads to the emergence of an isolated stationary state surrounded by multiple oscillatory states and cross-frequency coupling develops at the bifurcation points. We identify the possible network motifs that induce oscillations and examine how multiple oscillatory states come together to enrich the dynamical landscape.