Heterogeneity-induced competitive firing dynamics in balanced excitatory-inhibitory spiking neuron networks

Excitatory–inhibitory (E-I) balance is important to maintain normal working and functioning of neuron networks. Parameter heterogeneity exists ubiquitously in neuron systems and plays significant roles in modulating neuron functions. This work concentrates on competitive and collective spiking behaviors of E-I neuron networks by considering heterogeneities in intra-network, inter-network couplings, and excitability currents. Macroscopic order-parameter dynamics is analytically derived in terms of the Lorentz-ansatz (LA) approach for a large population of quadratic integrate-and-fire (QIF) neurons, which is proved to accurately demonstrate various collective firing behaviors. Collaborated firing bifurcations of both independent excitatory/inhibitory networks and the coupled E-I networks are explored, and a wealth of collaborative firing behaviors are unveiled in the presence of parameter disorders, such as the steady state, the limit-cycle oscillations, the quasi-periodicity, and the chaotic firing. The emergence of fast and slow oscillatory modes due to the competition between the excitatory and inhibitory neuron populations is revealed. This mechanism is successfully applied to analysis of the fast-slow mode transitions and complicated collective firing behaviors. These studies are expected to well facilitate the understandings of working principles of coupling disorder in E-I balanced neuron networks.