How to make the perturbation in a diffusion based mutualisti​c_lotka_vo​lterra

Hi,

Bellow I have attached a code which describes the behavior of two organisms presents in a system. This organisms diffuse throughout the medium due to presents of the Brownian motion in the medium. I need to extend this code with following feature.

need to setup a boundary condition of the regime of the both organisms and need to introduce a perturbation in the (ex. introducing a sinusoidal wave) space to analyse the behavior of the organisms due to this perturbation.

I would appreciate a lot if you could assist me of how to the coding to introduce this feature in the attached file