I want to solve the following set of equations. $$ \dot{x}(t) = -kx(t) + a x(t) + b y(t) + c x(t)y(t)\\ \dot{y}(t) = -py(t) - a x(t) - b y(t) - c x(t)y(t) $$
If $k=p=0$ it can be solved by noting $x+y=const$. In this case, the solutions are monotonous.
The related work I found was the method outlined in https://arxiv.org/abs/2012.14021, which does not apply.
I would appreciate suggestions and references!