This article is cited in 15 papers

On Entropy-Type Functionals Arising in Stochastic Chemical Kinetics Related to the Concentration of the Invariant Measure and Playing the Role of Lyapunov Functions in the Dynamics of Quasiaverages

A. V. Gasnikov, E. V. Gasnikova

Moscow Institute of Physics and Technology

Abstract: This paper studies the relationship between the Lyapunov function of a macrosystem whose dynamics is governed by the laws of stochastic chemical kinetics and the invariant measure of this macrosystem arising at large times. A necessary and sufficient condition for the reduction of the search problem for the equilibrium of the macrosystem (the most probable macrostate of the invariant measure of this macrosystem) to an entropy-linear programming problem is given.

Keywords: entropy-type functional, stochastic chemical kinetics, Lyapunov function, dynamics of quasiaverages, equilibrium search problem, invariant measure, predator-prey model, Lotka–Volterra system.

UDC: 519.2

Received: 03.08.2012
Revised: 21.02.2013

DOI: 10.4213/mzm10120

 English version: Mathematical Notes, 2013, 94:6, 854–861

Bibliographic databases:

• 
• 
• 
• 
• 
•