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Excitatory activity decays toward zero while a sigmoid of its net recurrent and external input replenishes it. The factor 1−r_E E reduces the responsive fraction as activity rises, and τ_E sets the time scale. The code applies an Euler step and clips the stored activity to [0,1].
Terms & definitions
| Term | Meaning in this source |
|---|---|
| E | Excitatory population activity |
| I | Inhibitory population activity |
| w_EE | Self-excitation weight |
| w_EI | Inhibitory influence |
| I_E | External excitatory input |
| tau_E | Time constant |
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Original context
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};
// ═══════════════════════════════════════════════════════════════════════════════
// LEVEL 2: NEURAL NETWORK / POPULATION MATHEMATICS
// ═══════════════════════════════════════════════════════════════════════════════
// Wilson-Cowan Equations (population dynamics)
// τ_E * dE/dt = -E + (1 - r_E*E) * S(w_EE*E - w_EI*I + I_E)
// τ_I * dI/dt = -I + (1 - r_I*I) * S(w_IE*E - w_II*I + I_I)
// where S(x) = 1/(1 + exp(-a*(x-θ))) is the sigmoid
struct WilsonCowan {
// Time constants (ms)
float tau_E = 10.0f;
float tau_I = 20.0f;
// Connection weights
float w_EE = 12.0f; // E → E
float w_EI = 4.0f; // I → E (inhibition of excitatory)Exact original notation
τ_E * dE/dt = -E + (1 - r_E*E) * S(w_EE*E - w_EI*I + I_E)