Variability of collective dynamics in random tree networks of strongly-coupled stochastic excitable elements
arXiv:1808.02750 · doi:10.1103/PhysRevE.98.052303
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.
arXiv comment15 Figures, 23 pages
References in corpus (15)
- Synchronization in complex networks
- The spread of epidemic disease on networks
- Emergent complex neural dynamics
- Optimal Dynamical Range of Excitable Networks at Criticality
- Diversity-induced resonance
- Crowd behaves as excitable media during Mexican wave
- Predicting criticality and dynamic range in complex networks: effects of topology
- Active dendrites enhance neuronal dynamic range
- Linking structure and activity in nonlinear spiking networks
- Traveling and pinned fronts in bistable reaction-diffusion systems on network
- Single-Neuron Criticality Optimizes Analog Dendritic Computation
- Statistical Physics approach to dendritic computation: The excitable-wave mean-field approximation
- Propagation failure of excitation waves on trees and random networks
- Emergence and coherence of oscillations in star networks of stochastic excitable elements
- Emergent stochastic oscillations and signal detection in tree networks of excitable elements