individuals can have different knowledge-like functions.

Individual Based Model
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Let $N$ be the number of individuals in the population. Each individual $i$ is associated with a knowledge-like function $k^i \in \mathcal F$.

\[def:Gamma\] A *structure matrix* $\Gamma = (\gamma_{ij})_{1\leq i,j \leq N}$ is a square matrix of size $N$ describing the influence that individuals have on each other. More precisely for each $(i,j)\in\{1,...,N\}^2, \gamma_{ij} \in {\mathbb{R}}$ describes the strength of the influence of $j$ on $i$.

\[rem:inertia\] For all $i \in \{1,...,N\}$ the greater the $\gamma_{ii}$, the less the individual $i$ will be influenced by others. So $\gamma_{ii}$ can be interpreted as the *inertia* of the individual $i$.

#### Examples of structure matrices.

-   We consider a population of $N$ individuals structured in age, sorted such that individual 1 is the youngest and $N$ the oldest. It has been shown that older individuals tend to have a higher inertia [@Gopnik7892], which can be modelled by the condition $\gamma_{11} < ... < \gamma_{NN}$.

-   Let us consider the relationship between a parent and her offspring. The offspring learns a lot from her parent but the situation is not symmetric. Let $s \in (0,1)$ describes the influence of a parent on 