Interactive Stability & Network Model

We consider the following McKean-Vlasov equation:

\begin{aligned} d V_{t}^{μ} & = b (V_{t}^{μ}) d t + J E [X_{t}^{μ} f (V_{t}^{μ})] d t - V_{t -}^{μ} \int_{R_{+}} 1_{{z \leq f (V_{t -}^{μ})}} N (d t, d z), \\ d X_{t}^{μ} & = \frac{1 - X_{t}^{μ}}{τ} d t - U X_{t -}^{μ} \int_{R_{+}} 1_{{z \leq f (V_{t -}^{μ})}} N (d t, d z), \end{aligned}

where

b (v) = m - λ v

, and

f (v) = v^{2}

f (v) = v^{1 / β}

f (v) = \frac{1}{β} 1_{v \geq 1}

Initial Distribution

a (Max Initial V₀)

Target α (From Tab 3)

Burn-in Time (T)

J (Coupling)

N (Neurons)

T (Duration)

dt (Step)

Interactive: Click anywhere on the computed curve to automatically select an $α$ value and jump to Stability Analysis!

α Min

α Max

Points

Target α (Alpha)

ω₀ (Integration Boundary)

Points

Computing Complex ODEs...

Mean-Field of 2D Spiking Neurons