Read the equation
For fixed coherence and free energy, the Ω derivative of the displayed objective is 2(Ω−Ω*). The body multiplies its negative by a rate and Ω(1−Ω), then adds further coherence and free-energy terms. These modifications mean it is not simply the Euclidean negative gradient of the displayed V, so monotonic decrease needs a separate calculation.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| Omega | State variable |
| V | Candidate objective |
| Omega_star | Target value |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
}
// dV/dt = (V(t) - V(t-1))/dt
inline double lyapunov_derivative(double v_curr, double v_prev, double dt = 0.1) {
return (v_curr - v_prev) / dt;
}
// Gradient flow: dΩ/dt = -∇V(Ω)
inline double gradient_flow(double omega, double coherence, double free_energy) {
double grad_omega = 2.0 * (omega - TARGET_OMEGA);
double flow = -GRADIENT_ETA * grad_omega * omega * (1.0 - omega);
double coh_term = 0.001 * (1.0 - coherence);
double fe_term = 0.0005 * free_energy;
return flow + coh_term - fe_term;
}
// Check Lipschitz continuity
inline bool check_lipschitz(double fx, double fy, double x, double y, double L = LIPSCHITZ_BOUND) {Exact original notation
Gradient flow: dΩ/dt = -∇V(Ω)