Abstract
We analyze the collective dynamics of hierarchically structured networks of densely connected spiking neurons. These networks of sub-networks may represent interactions between cell assemblies or different nuclei in the brain. The dynamical activity pattern that results from these interactions depends on the strength of synaptic coupling between them. Importantly, the overall dynamics of a brain region in the absence of external input, so called ongoing brain activity, has been attributed to the dynamics of such interactions. In our study, two different network scenarios are considered: a system with one inhibitory and two excitatory subnetworks, and a network representation with three inhibitory subnetworks. To study the effect of synaptic strength on the global dynamics of the network, two parameters for relative couplings between these subnetworks are considered. For each case, a bifurcation analysis is performed and the results have been compared to large-scale network simulations. Our analysis shows that Generalized Lotka-Volterra (GLV) equations, well-known in predator-prey studies, yield a meaningful population-level description for the collective behavior of spiking neuronal interaction, which have a hierarchical structure. In particular, we observed a striking equivalence between the bifurcation diagrams of spiking neuronal networks and their corresponding GLV equations. This study gives new insight on the behavior of neuronal assemblies, and can potentially suggest new mechanisms for altering the dynamical patterns of spiking networks based on changing the synaptic strength between some groups of neurons.
Highlights
Networks of pulse-coupled units that operate with a threshold mechanism abound
We compare our analytical treatment of the Generalized Lotka-Volterra (GLV) equations with spiking network simulations for both examples considered in this paper, i.e. excitatory subnetworks and one inhibitory subnetwork (EEI) and inhibitory subnetworks was considered (III) networks
We focused on the role of the strength of couplings between subnetworks for global network dynamics
Summary
Networks of pulse-coupled units that operate with a threshold mechanism abound. Examples are forest fires, swarms of flashing fireflies, earthquakes and interacting spiking neurons. It is believed that the neocortex has a modular structure with modules that are similar in overall design and operation but different in cell types and connectivity[1] This conceptualizes the brain as a hierarchical network of subnetworks that interact with each other, and as a consequence, build a functional brain. Due to spike timing synaptic plasticity, pre-synaptic neurons that fire together within a close time frame with post-synaptic neurons strengthen synaptic connections that eventually results in formation of cell assemblies[2]. Neurons in these assemblies can be connected via short or long range synapses The interaction of these assemblies may shape an ongoing brain activity that exists even in the absence of external inputs, and may correlate with some internal cognitive states[3]. Wilson-Cowan equations[10] are a prime candidate for such analysis
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