# Time Integration of a nonlinear reaction-diffusion system

I want to solve the following system of nonlinear reaction-diffusion equations (Schnakenberg Turing) using FEM methods (such as deal.ii):

$$\partial_{t} u = \Delta u + \gamma\left(a-u+u²v\right)$$ $$\partial_{t} v = d\Delta v + \gamma\left(b-u²v\right)$$

where d, $\gamma$, a, b being constants.

Probably I need to first apply a time integration scheme (such as Crank-Nicholson, implicit Runge-Kutta), and then FE space discretization.

Question: How should I choose and perform the time integration for this nonlinear system? Any hints for very similar examples or specific literature?