Synchronization of interacted spiking neuronal networks with inhibitory coupling

Abstract

• The synchronization index (SI) in two large interacted via inhibitory coupling networks oscillates periodically in time; the time intervals of high SI alternates with the time intervals of low SI. • The synchronization indexes in these networks exhibit either inphase or antiphase synchronization depending on the inhibitory coupling strength between them. We suppose that the underlying mechanism behind the antiphase dynamics lies in the cognitive resource redistribution between neuronal ensembles in the brain. • Excitatory coupling between the neurons inside the network affects the synchronization index. To maintain the neural network in the regimes of inphase or antiphase SI oscillations, we should keep a balance between excitatory and inhibitory connections. It suggests that the excitatory and the inhibitory currents should compensate each other. In other words, when one of them increases, the other must be increased too, and vice versa. • The coupling inside the input small network affects antiphase synchronization between two large networks. However, the scenario from positive and negative correlation and back between the large networks are only determined by inhibitory coupling between them. The development of mathematical models to describe neuronal interaction processes in the brain is a challenging task of nonlinear dynamics. Recent advances in biochemistry and neuroscience allow better understanding of biological mechanisms underlying the neuron functioning and synaptic connections between neurons. Moreover, significant progress in brain imaging sheds light on the structure of the brain network and certain aspects of neuronal dynamics. However, dynamical mechanisms leading to synchronization between different brain areas still remain unknown and require further investigation. To shed light on this issue, we consider two small-world networks of Hodgkin-Huxley neurons interacting via inhibitory coupling. We found that synchronization indices (SI) in both networks oscillate periodically in time, so that time intervals of high SI alternate with time intervals of low SI. Depending on the coupling strength, the two coupled networks can be in the regime of either in-phase or anti-phase synchronization. We suppose that the inherent mechanism behind such a behavior lies in the cognitive resource redistribution between neuronal ensembles of the brain.