Lyapunov Function Partial Differential Equations for Chemical Reaction Networks: Some Special Cases

Abstract

In this paper, we develop a method to generate the Lyapunov function for stability analysis for chemical reaction networks. Based on the Chemical Master Equation, we derive the Lyapunov Function partial differential equations (PDEs), whose solution approximates the scaling non-equilibrium potential and serves as the candidate Lyapunov function for the given network. We further prove that for any chemical reaction network the solution (if exists) of the PDEs is dissipative. Moreover, the proposed method of Lyapunov Function PDEs is qualified for analyzing the asymptotic stability of complex balanced networks, all networks with $1$-dimensional stoichiometric subspace and some special networks with more than $2$-dimensional stoichiometric subspace if some moderate conditions are added. Several examples are presented to illustrate the efficiency of the method.

References in corpus (2)

• Finding complex balanced and detailed balanced realizations of chemical reaction networks
• New Approach to the Stability of Chemical Reaction Networks: Piecewise Linear in Rates Lyapunov Functions

Cited by in corpus (7)

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• Lyapunov Function PDEs Method to the Stability of Some Chemical Reaction Networks
• Persistence of Delayed Complex Balanced Chemical Reaction Networks
• Hamilton-Jacobi-Bellman equations for Chemical Reaction Networks
• Lyapunov Function Partial Different Equations for Stability Analysis of a C of Chemical Reaction Networks
• Some dynamical properties of delayed weakly reversible mass-action systems
• A graphic formulation of non-isothermal chemical reaction systems and the analysis of detailed balanced networks