Read the equation
The next state keeps 95% of x and incorporates 5% of dx_norm. It converges to a constant input with error factor 0.95 per update. It becomes a network consensus mechanism only if the supplied input is appropriately constructed from other agents and the resulting network weights satisfy the relevant convergence conditions.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| x | Current local state |
| dx_norm | Externally supplied averaging target |
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
## 3.9 Family 8: Consensus Averaging ``` f₈(x) = 0.95 · x + 0.05 · dx_norm ``` **Equation Type**: Consensus protocol: x_i(t+1) = x_i(t) + Σ(x_j - x_i) **Explanation**: Slowly integrates external signals while maintaining strong memory. Used for reaching agreement across distributed processes. ## 3.10 Family 9: Swarm Interaction ``` f₉(x) = x + 0.05 · softsign(dx_norm - x) ``` **Equation Type**: Swarm force: x_i = Σ f(x_j - x_i) **Explanation**: Models attraction/repulsion dynamics between agents. The softsign creates bounded forces that prevent collapse or explosion. ## 3.11 Family 10: Field Accumulator ``` ρ = 1 / (1 + φ)
Exact original notation
f₈(x) = 0.95 · x + 0.05 · dx_norm