Interaction Force on an Individual

Available identifiers

interaction force on an individual

The interaction force on individual i is given by a weighted sum of attractive forces from all other connected individuals j, the respective media and the respective influencer scaled by the parameters a,b,c > 0 respectively.

Defining Formula: $F_{i} (𝐱, 𝐲, 𝐳, t) = \frac{a}{\sum_{j^{'}} w_{i j^{'}} (t)} \sum_{j = 1}^{N} w_{i j} (t) (x_{j} (t) - x_{i} (t)) + b \sum_{m = 1}^{M} B_{i m} (t) (y_{m} (t) - x_{i} (t)) + c \sum_{l = 1}^{L} C_{i l} (t) (z_{l} (t) - x_{i} (t))$
$B (t)$ symbol represents Medium Follower Matrix
$C (t)$ symbol represents Influencer Individual Matrix
$F_{i} (t)$ symbol represents Interaction Force
$a$ symbol represents Parameter to Scale Attractive Force from Other Individuals
$b$ symbol represents Parameter to Scale Attractive Force from Media
$c$ symbol represents Parameter to Scale Attractive Force from Influencers
$t$ symbol represents Time
$w_{i j}$ symbol represents Interaction Weight