WILSON-COWAN POPULATION DYNAMICS · where S(x)

Read the equation

This relation defines where S(x) in the source section “WILSON-COWAN POPULATION DYNAMICS · where S(x)”. Applies an exponential factor. The exponent determines its real scaling or, for a complex exponent, its phase. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read where S(x) as the quantity being defined or updated by this relation.

2. Applies an exponential factor. The exponent determines its real scaling or, for a complex exponent, its phase.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

• This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.

Original context

/**
 * WilsonCowanPopulation - Neural population dynamics
 *
 * Implements:
 *   dE/dt = -E + S(w_EE*E - w_EI*I + I_ext)
 *   dI/dt = -I + S(w_IE*E - w_II*I)
 *
 * where S(x) = 1/(1 + exp(-a*(x - theta)))
 */
class WilsonCowanPopulation {
public:
    double E;  // Excitatory population activity
    double I;  // Inhibitory population activity

    // Connection weights
    double w_EE;  // E -> E
    double w_EI;  // I -> E (inhibitory)
    double w_IE;  // E -> I

where S(x) = 1/(1 + exp(-a*(x - theta)))

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