Despite what graphical representation can suggest, biological networks are deeply dynamic objects. Such a feature reflects the mutual, intricate time-dependency of activities associated to network nodes. Within this frame, questions like stability, robustness, time response to external stimuli are of particular importance.

At the mathematical stage, networks are described in terms on linearized system of ordinary differential equations (ODE's). The main problem with such a model is that reliable measures of quantitative level of activity corresponding to each node are seldomly available, where the dynamical behavior depends strongly on these parameter values.

While for extremely small networks pure parametric analysis of stability can be derived in a full analytic way, the same is unfeasible for larger networks. Therefore, we thoroughly investigate the ODE system within a wide range of relevant parameter values, mainly to infer statistical information about dynamical behavior of the object at hand.

Since even the minimum information about connectivity sign (inhibition/activation) gives rise to a set of configurations growing with exponential rate, stability analysis necessarily calls into play optimized computational tools. To this aim, we have implemented parallel algorithms based on state-of-the-art techniques for eigenvalue analysis, like iterative Arnoldi methods, merged with highly efficient cache-based routines for low-level linear algebra operations.

This allow us to systematically test the dynamic behavior of small- and medium-scale networks, while large-scale ones (with order of thousands of nodes) can be approached by classical Monte Carlo methods.