Related papers: Robust Lyapunov Functions for Reaction Networks: A…
Piecewise-Linear in Rates (PWLR) Lyapunov functions are introduced for a class of Chemical Reaction Networks (CRNs). In addition to their simple structure, these functions are robust with respect to arbitrary monotone reaction rates, of…
We consider the relationship between stationary distributions for stochastic models of reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well known Lyapunov function of reaction…
We investigate a broad family of chemical reaction networks (CRNs) assigned with mass action kinetics, called complex-balanced-produced-CRNs (CBP-CRNs), which are generated by any given complex balanced mass action system (MAS) and whose…
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…
Much of the theory on chemical-reaction networks (CRNs) has been developed in the ideal-solution limit, where interactions between the solutes are negligible. However, there is a large variety of phenomena in biological cells and…
In this paper the qualitative dynamical properties of so-called generalized ribosome flow models are studied. Ribosome flow models known from the literature are generalized by allowing an arbitrary directed network structure between the…
Quadratic Lyapunov functions are prevalent in stability analysis of linear consensus systems. In this paper we show that weighted sums of convex functions of the different coordinates are Lyapunov functions for irreducible consensus…
In 1961, R\'enyi discovered a rich family of non-classical Lyapunov functions for kinetics of the Markov chains, or, what is the same, for the linear kinetic equations. This family was parameterised by convex functions on the positive…
In this paper, we propose a novel technique, referred to as the Lyapunov Function PDEs technique, to diagnose persistence of chemical reaction networks with mass-action kinetics. The technique allows that every network is attached to a…
This work studies the problem of searching for homogeneous polynomial Lyapunov functions for stable switched linear systems. Specifically, we show an equivalence between polynomial Lyapunov functions for systems of this class and quadratic…
Motivation: A Chemical Reaction Network (CRN) is a set of chemical reactions, which can be very complex and difficult to analyze. Indeed, dynamical properties of CRNs can be described by a set of non-linear differential equations that…
This paper studies the use of vector Lyapunov functions for the design of globally stabilizing feedback laws for nonlinear systems. Recent results on vector Lyapunov functions are utilized. The main result of the paper shows that the…
We consider delayed chemical reaction networks with generalized kinetics of product form and show that complex balancing implies that within each positive stoichiometric compatibility class there is a unique positive equilibrium that is…
A class of chemical reaction networks is described with the property that each positive equilibrium is locally asymptotically stable relative to its stoichiometry class, an invariant subspace on which it lies. The reaction systems treated…
This paper considers a wide class of smooth continuous dynamic nonlinear systems (control objects) with a measurable vector of state. The problem is to find a special function (Lyapunov function), which in the framework of the second…
In this work we addressed the problem of stability analysis for an uncertain piecewise affine model of a genetic regulatory network. In particular we considered polytopic parameter uncertainties on the proteins production rate functions,…
The study of the dynamics of chemical reactions, and in particular phenomena such as oscillating reactions, has led to the recognition that many dynamical properties of a chemical reaction can be predicted from graph theoretical properties…
A numerically effective procedure for determining weakly reversible chemical reaction networks that are linearly conjugate to a known reaction network is proposed in this paper. The method is based on translating the structural and…
Recently, A.N. Gorban presented a rich family of universal Lyapunov functions for any linear or non-linear reaction network with detailed or complex balance. Two main elements of the construction algorithm are partial equilibria of…
We propose a unified framework that allows for the full mechanistic reconstruction of chemical reaction networks (CRNs) from concentration data. The framework utilizes an integral formulation of the differential equations governing the…