Solve ODE $\dot x_{i}=\frac{1}{card(S_i)} \sum_{j\in S_i} I(x_{j},x_{i})\quad \quad (1)$

Question

Let us consider continuous functions $x_j=x_j(t):[0,T] \to [-1,1]$, where $T>0$ and $j\in\{1,\dots,n\}$. Let also $i\in\{1,\dots,n\}$ and consider: $$\dot x_{i}=\frac{1}{card(S_i)} \sum_{j\in S_i} I(x_{j},x_{i})\quad \quad (1)$$ where $S_i$ is an arbitrary proper subset of $\{1,\dots,n\}$ and $$\label{cont_vs_lead} I(x_{j},x_{i})=\begin{cases} x_{i} & \qquad i\in \mathcal{P} \\ r & \qquad i\in \mathcal C \\ \frac{x_{j}-x_{i}}{2} & \qquad i \notin \mathcal C \cup \mathcal{P} \end{cases}$$ Here $r\in[-1,1]$, while $\mathcal C$, $\mathcal{P}$ are proper subsets of $\{1,\dots,n\}$. Is it possible to solve analytically ODE (1).