Reduction of chemical reaction networks using quasi-integrals.

摘要: We present a numerical method to identify possible candidates for quasi-stationary manifolds in complex reaction networks governed by systems of ordinary differential equations. Inspired singular perturbation theory, we examine the ratios certain components rate vector. Those that rapidly approach nearly constant value define slow manifold original flow terms quasi-integrals, is, functions are along trajectories. The dimensionality system is thus effectively reduced without reliance on priori knowledge different time scales system. also demonstrate relation our theory which, its simplest form, just well-known quasi-steady-state approximation. In two case studies, apply oscillatory chemical systems: 6-dimensional hemin-hydrogen peroxide-sulfite pH oscillator and 10-dimensional mechanistic model peroxidase-oxidase (PO) conjecture presented especially suited straightforward reduction higher dimensional dynamical where analytical methods fail associated with invariant