Algorithmic modeling and analysis of nonlinear biological systems

This paper proposes an algorithmic modeling and analysis method to study the dynamics of nonlinear biological systems. Motivated by the recent use of piecewise affine models in reachability analysis of continuous dynamical systems, we propose a multi-affine approximation method to study biological system models defined on hyperrectangle. We show that such approximation is useful for constructing system´s abstraction in form of finite state transition system models whose properties can be verified algorithmically using model checking formalism. An example use of the proposed method to study the robustness of a biological system model to parameter variation is presented.