Coexistence of asynchronous and clustered dynamics in noisy inhibitory neural networks

A regime of coexistence of asynchronous and clustered dynamics is analyzed for globally coupled homogeneous and heterogeneous inhibitory networks of quadratic integrate-and-fire (QIF) neurons subject to Gaussian noise. The analysis is based on accurate extensive simulations and complemented by a mean-field description in terms of low-dimensional next generation neural mass models for heterogeneously distributed synaptic couplings. The asynchronous regime is observable at low noise and becomes unstable via a sub-critical Hopf bifurcation at sufficiently large noise. This gives rise to a coexistence region between the asynchronous and the clustered regime. The clustered phase is characterized by population bursts in the {\gamma}-range (30-120 Hz), where neurons are split in two equally populated clusters firing in alternation. This clustering behaviour is quite peculiar: despite the global activity being essentially periodic, single neurons display switching between the two clusters due to heterogeneity and/or noise.