Finding complex balanced and detailed balanced realizations of chemical reaction networks

Abstract

Reversibility, weak reversibility and deficiency, detailed and complex balancing are generally not "encoded" in the kinetic differential equations but they are realization properties that may imply local or even global asymptotic stability of the underlying reaction kinetic system when further conditions are also fulfilled. In this paper, efficient numerical procedures are given for finding complex balanced or detailed balanced realizations of mass action type chemical reaction networks or kinetic dynamical systems in the framework of linear programming. The procedures are illustrated on numerical examples.

submitted to J. Math. Chem

References in corpus (4)

• Invariant grids for reaction kinetics
• Nonpolynomial vector fields under the Lotka-Volterra normal form
• Maximal and minimal realizations of reaction kinetic systems: computation and properties
• How far is complex balancing from detailed balancing?

Cited by in corpus (26)

• A geometric approach to the Global Attractor Conjecture
• Lyapunov Function Partial Differential Equations for Chemical Reaction Networks: Some Special Cases
• Dynamical Equivalence and Linear Conjugacy of Chemical Reaction Networks: New Results and Methods
• General H-theorem and entropies that violate the second law
• Uniqueness of feasible equilibria for mass action law (MAL) kinetic systems
• Finding weakly reversible realizations of chemical reaction networks using optimization
• A computational approach to the structural analysis of uncertain kinetic systems
• Local Equivalence of Reversible and General Markov Kinetics
• Complex Balancing Reconstructed to the Asymptotic Stability of Mass-action Chemical Reaction Networks with Conservation Laws
• Energy and entropy on irreversible chemical reaction-diffusion systems with asymptotic stability
• New universal Lyapunov functions for non-linear reaction networks
• The disguised toric locus and affine equivalence of reaction networks
• Finding Thermodynamically Favorable Pathways in Chemical Reaction Networks Using Flows in Hypergraphs and Mixed-Integer Linear Programming
• Demystification of Entangled Mass Action Law
• Diffusion-dynamics laws in stochastic reaction networks
• Linear Conjugacy of Chemical Reaction Networks
• Lyapunov Function PDEs Method to the Stability of Some Chemical Reaction Networks
• Disguised toric dynamical systems
• Single-Target Networks
• ReactionKinetics - A Mathematica package with applications II. Computational problems when building a reaction kinetics package
• A Linear Programming Approach to Weak Reversibility and Linear Conjugacy of Chemical Reaction Networks
• A graphic formulation of non-isothermal chemical reaction systems and the analysis of detailed balanced networks
• Lyapunov Function Partial Different Equations for Stability Analysis of a C of Chemical Reaction Networks
• Three waves of chemical dynamics
• Automatic model generation
• Realizations of kinetic differential equations