Read the equation
Each agent adds a sum of differences between neighbor states and its own state. Coupling weights, the neighbor graph, and step-size restrictions determine whether agents converge to consensus. With unrestricted unit weights, the written sum can overshoot and does not guarantee averaging behavior.
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
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)
Exact original notation
Consensus protocol: x_i(t+1) = x_i(t) + Σ(x_j - x_i)