Multi-node excitable network using FHN reductions of HH dynamics: chain/ring topology, sigmoidal synaptic coupling, propagation delay, pacer-driven waves, and bursting-like activity.
This is a fast FHN network, not a full conductance-based HH network. It keeps the HH excitability geometry while making multi-node propagation interactive.
Live graphs
About this model
This simulator builds a small excitable-neuron network from FitzHugh-Nagumo reductions of Hodgkin-Huxley dynamics. Each node has a fast voltage-like variable v and a slow recovery variable w. Node 0 receives a pulse, rhythmic pacer, or tonic drive, and neighboring nodes receive a sigmoidal excitatory synaptic current g S(v_j)(E_syn−v_i). With weak coupling, excitation may stay local; with stronger coupling, spikes propagate down a chain or around a ring. Rhythmic pacing can create repeated waves and bursting-like population activity. The selected-node traces show propagation from first to middle to last node, the activity panel overlays mean voltage with spike times, and the phase portrait shows the slow-fast loop of the stimulated node.
Who it's for: Students in computational neuroscience, biophysics, nonlinear dynamics, or applied math learning excitable media, synaptic coupling, and propagation before full conductance-based network models.
Key terms
Hodgkin-Huxley
FitzHugh-Nagumo
Excitable network
Synaptic coupling
Propagation delay
Spike raster
Bursting
Slow-fast dynamics
How it works
A coupled excitable-neuron network using FitzHugh-Nagumo reductions of Hodgkin-Huxley dynamics: local synaptic coupling supports propagation, rhythmic pacemaking, and bursting-like population activity.
Key equations
v̇_i = v_i − v_i³/3 − w_i + I_i + Σ g S(v_j)(E_syn−v_i), ẇ_i = ε(v_i+a−bw_i). Here S(v)=1/(1+e^{-8(v−θ)}).
Frequently asked questions
Why use FitzHugh-Nagumo instead of full Hodgkin-Huxley at every node?
Full HH networks are heavier and expose many channel parameters. FHN keeps the essential slow-fast excitability geometry, so propagation and synchronization can be explored interactively with many nodes.
What does the propagation delay measure?
It is the time between the first threshold crossing of node 0 and the first threshold crossing of the last node. If the last node never spikes, propagation failed.
Is the bursting biologically exact?
No. The page shows bursting-like population episodes from rhythmic drive and recurrent propagation, not a detailed ionic bursting model with calcium or adaptation currents.