The effects of degree distributions in random networks of Type-I neurons
arXiv:2104.14666 · doi:10.1103/PhysRevE.103.052305
Abstract
We consider large networks of theta neurons and use the Ott/Antonsen ansatz to derive degree-based mean field equations governing the expected dynamics of the networks. Assuming random connectivity we investigate the effects of varying the widths of the in- and out-degree distributions on the dynamics of excitatory or inhibitory synaptically coupled networks, and gap junction coupled networks. For synaptically coupled networks, the dynamics are independent of the out-degree distribution. Broadening the in-degree distribution destroys oscillations in inhibitory networks and decreases the range of bistability in excitatory networks. For gap junction coupled neurons, broadening the degree distribution varies the values of parameters at which there is an onset of collective oscillations. Many of the results are shown to also occur in networks of more realistic neurons.
arXiv commentTo appear in Physical Review E
References in corpus (23)
- The structure and function of complex networks
- Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
- Solvable model for chimera states of coupled oscillators
- Long Time Evolution of Phase Oscillator Systems
- Macroscopic description for networks of spiking neurons
- Stability diagram for the forced Kuramoto model
- Low-dimensional dynamics of populations of pulse-coupled oscillators
- Dynamics of noisy oscillator populations beyond the Ott-Antonsen ansatz
- Non-universal results induced by diversity distribution in coupled excitable systems
- Exact mean-field theory explains the dual role of electrical synapses in collective synchronization
- A reduction methodology for fluctuation driven population dynamics
- An exact firing rate model reveals the differential effects of chemical versus electrical synapses in spiking networks
- Mean field theory of assortative networks of phase oscillators
- Stochastic cellular automata model of neural networks
- Collective mode reductions for populations of coupled noisy oscillators
- Enhancing neural-network performance via assortativity
- Coherent periodic activity in excitatory Erdos-Renyi neural networks:The role of network connectivity
- Synchronization scenarios in the Winfree model of coupled oscillators
- Modeling the Network Dynamics of Pulse-Coupled Neurons
- Ott-Antonsen ansatz is the only admissible truncation of a circular cumulant series
- The effects of within-neuron degree correlations in networks of spiking neurons
- Circular Cumulant Reductions for Macroscopic Dynamics of Kuramoto Ensemble with Multiplicative Intrinsic Noise
- Stochastic bursting in unidirectionally delay-coupled noisy excitable systems