In this paper a novel computational technique for finite discrete approximation of continuous dynamical systems suitable for a significant class of biochemical dynamical systems is introduced. The method is parameterized in order to affect the imposed level of approximation provided that with increasing parameter value the approximation converges to the original continuous system. By employing this approximation technique, we present algorithms solving the reachability problem for biochemical dynamical systems. The presented method and algorithms are evaluated on several exemplary biological models and on a real case study. This is a full version of the paper published in the proceedings of CompMod 2011.
In this article, we describe some recent results on the hybridization methods for the analysis of nonlinear systems. The main idea of our hybridization approach is to apply the hybrid systems methodology as a systematic approximation method. More concretely, we partition the state space of a complex system into regions that only intersect on their boundaries, and then approximate its dynamics in each region by a simpler one. Then, the resulting hybrid system, which we call a hybridization, is used to yield approximate analysis results for the original system. We also prove important properties of the hybridization, and propose two effective hybridization construction methods, which allow approximating the original nonlinear system with a good convergence rate. In this paper we describe reachability computation for continuous and hybrid systems and its potential contribution to the process of building and debugging biological models. We then develop a novel algorithm for computing reachable states for nonlinear systems and report experimental results obtained using a prototype implementation. We believe these results constitute a promising contribution to the analysis of complex models of biological systems.