This paper tackles theoretically the question of the structural stability of biological regulation networks subjected to the influence of their environment. The model of networks considered is that of threshold Boolean automata networks that take place amongst the pertinent models for both neural and genetic regulation networks. Diving this study into the context of two-dimensional cellular automata on Z2 and modelling their environment by boundary conditions, this work analyses the dynamical behaviours of new kinds of threshold networks, namely stochastic nonlinear networks. Through an approach at the frontier between discrete dynamical system theory, probability theory and theoretical computer science combining formal and computer-assisted methods, we present under which specific characteristics of their parametric structure the dynamics of such networks in the attractive case is drastically subjected to the power of their environment.