Need help to characterize a system of difference equations

Question

I am biologist, no mathematician. I have a system of difference equations of the form: $$ X_t^{(i)}=\sum_{j^+=1}^{m_{j^+}}{k_{j^+}^{(i)} Pa(X^{(i)})_{t-1}^{(j^+)}} * (1-\sum_{j^-=1}^{l_{j^-}}{k_{j^-}^{(i)}Pa(X^{(i)})_{t-1}^{(j^-)}}) $$ where $Pa(X^{(i)})$ is the set of parent variables of $X^{(i)}$. It also contains non-linear functions (Boolean continuous) I would like to find the numerical and topological constrains under which this system converge to a unique steady-state. I need more that just advice, I need a collaboration for my project. The first paper has been accepted. Showing convergence to a unique solution would validate my approach, showing equivalence, even partial, to probabilistic Boolean networks systems would make another paper. Thanks