Variability of collective dynamics in random tree networks of strongly-coupled stochastic excitable elements

Abstract

We study the collective dynamics of strongly diffusively coupled excitable elements on small random tree networks. Stochastic external inputs are applied to the leaves causing large spiking events. Those events propagate along the tree branches and, eventually, exciting the root node. Using Hodgkin-Huxley type nodal elements, such a setup serves as a model for sensory neurons with branched myelinated distal terminals. We focus on the influence of the variability of tree structures on the spike train statistics of the root node. We present a statistical description of random tree network and show how the structural variability translates into the collective network dynamics. In particular, we show that in the physiologically relevant case of strong coupling the variability of collective response is determined by the joint probability distribution of the total number of leaves and nodes. We further present analytical results for the strong coupling limit in which the entire tree network can be represented by an effective single element.

Dynamics of Reaction-Diffusion Oscillators in Star and other Networks with Cyclic Symmetries Exhibiting Multiple Clusters

“…1, and show how dynamics predictably depart from this simple anti-phase synchrony by varying k. Star networks have been considered in theoretical [26] and experimental studies on electronic networks [27], but never in natural systems. Star networks are an important naturally occurring motif in neural networks that perform cognitive [28][29][30] and sensorial functions [31], but living neural networks have too many unknown parameters to enable disentangling the roles of oscillator dynamics and network topology on emergent behavior.…”