Geometric analysis of synchronization in neuronal networks with global inhibition and coupling delays.

ABSTRACT: We study synaptically coupled neuronal networks to identify the role of coupling delays in network synchronized behaviour. We consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory and one inhibitory, are coupled with time-delayed synapses. The excitatory population is uncoupled, while the inhibitory population is tightly coupled without time delay. A geometric singular perturbation analysis yields existence and stability conditions for periodic solutions where the excitatory cells are synchronized and different phase relationships between the excitatory and inhibitory populations can occur, along with formulae for the periods of such solutions. In particular, we show that if there are no delays in the coupling, oscillations where the

SUBMITTER: Ryu H 

PROVIDER: S-EPMC6661332 | biostudies-literature | 2019 Sep

REPOSITORIES: biostudies-literature