FitzHugh-Nagumo

The FitzHugh-Nagumo rule is a two-variable spiking neuron model that captures the basic dynamics of an action potential. It models a neuron’s voltage and a recovery variable, producing realistic spike-like behavior.

The neuron’s state is described by two coupled differential equations:

\[\frac{dv}{dt} = v - \frac{v^3}{3} - w + I \\ \frac{dw}{dt} = a(bv + 0.7 - c w)\]

Where:

• \(v\) is the membrane potential (activation).
• \(w\) is a recovery variable.
• \(I\) is total input: external input, background current, and optional noise.
• \(a, b, c\) are model parameters controlling the shape and timing of spikes.
• A spike is recorded when \(v \geq \text{threshold}\).

The rule models oscillatory behavior, rest states, and excitability, and is commonly used in computational neuroscience to simulate spiking behavior without the complexity of full Hodgkin-Huxley dynamics.

Parameters

• A (Recovery Rate): Controls how strongly the recovery variable responds to changes in voltage.
• B (Rec. Voltage Dependence): Scales how much voltage affects the recovery dynamics.
• C (Rec. Self Dependence): Determines how quickly the recovery variable returns to baseline.
• Spike Threshold: If the voltage exceeds this value, the neuron is considered to have spiked.
• Background Current: Constant input current applied to the neuron.

For all other parameters, see common neuron properties