The Experts below are selected from a list of 3246 Experts worldwide ranked by ideXlab platform
Peter Hanggi - One of the best experts on this subject based on the ideXlab platform.
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what can be stated by the Glansdorff prigogine criterion concerning the stability of mass action kinetic systems
Journal of Chemical Physics, 1999Co-Authors: Thomas Wilhelm, Peter HanggiAbstract:We investigate which general results concerning the local stability of steady states of arbitrary chemical reaction networks can be deduced with the Glansdorff–Prigogine stability criterion. Especially, it is proven that the presence of an autocatalytic reaction is not a necessary condition for a violation of the thermodynamic stability condition. It turns out that every reaction with at least one variable reactant at each side of the reaction equation can potentially destabilize the steady states. An explicit example of a simple reaction system without autocatalytic reactions where the stability of the steady state changes via a supercritical Hopf bifurcation is discussed. Furthermore, in expanding the original concept for proving local stability to global stability analyses, a general way for constructing different Lyapunov functions is given.
Oliver Sawodny - One of the best experts on this subject based on the ideXlab platform.
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the Glansdorff prigogine stability criterion for biochemical reaction networks
Automatica, 2011Co-Authors: Michael Ederer, Ernst Dieter Gilles, Oliver SawodnyAbstract:Local stability analysis of steady states in mathematical models of biochemical reaction networks is an important tool for systems biology. The second variation of the Gibbs energy around a steady state is a positive definite function and a candidate for a Lyapunov function. A sufficient condition for the local stability is the local negative definiteness of the time derivative of this function. This is expressed by the Glansdorff-Prigogine stability criterion. Previously, the criterion was criticized to be overly conservative and difficult to check. Here, we derive an easily testable form of the criterion for models of biochemical networks. The criterion can be evaluated with incomplete knowledge of the parameters. For ideal mass-action kinetics, it depends only on the steady state fluxes. For reaction systems in ideal solutions, the Glansdorff-Prigogine criterion is overly conservative and we give a tighter criterion that depends on the same subset of the parameters as the Glansdorff-Prigogine criterion. Whenever these criteria are indefinite, there exist parameter values such that the steady state is unstable. By means of simple example systems we explore these aspects and discuss the possible uses of the criteria for systems biology.
Thomas Wilhelm - One of the best experts on this subject based on the ideXlab platform.
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what can be stated by the Glansdorff prigogine criterion concerning the stability of mass action kinetic systems
Journal of Chemical Physics, 1999Co-Authors: Thomas Wilhelm, Peter HanggiAbstract:We investigate which general results concerning the local stability of steady states of arbitrary chemical reaction networks can be deduced with the Glansdorff–Prigogine stability criterion. Especially, it is proven that the presence of an autocatalytic reaction is not a necessary condition for a violation of the thermodynamic stability condition. It turns out that every reaction with at least one variable reactant at each side of the reaction equation can potentially destabilize the steady states. An explicit example of a simple reaction system without autocatalytic reactions where the stability of the steady state changes via a supercritical Hopf bifurcation is discussed. Furthermore, in expanding the original concept for proving local stability to global stability analyses, a general way for constructing different Lyapunov functions is given.
D.d. Majumder - One of the best experts on this subject based on the ideXlab platform.
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From neurocomputation to immunocomputation - a model and algorithm for fluctuation-induced instability and phase transition in biological systems
IEEE Transactions on Evolutionary Computation, 2002Co-Authors: R. Kozma, D.d. MajumderAbstract:Explores bioinformatics-based modeling of immunological instabilities. We develop an algorithm for analyzing stability-instability properties of complex systems and use the developed technique to induce transitions in physical, biological and engineering systems. As a case study, we analyze the phenomena of tumor destabilization or spontaneous biological regression of a malignant focus-lymphocyte interactive system. Using stochastic noise analysis, we model high-dimensional collective oscillations of nonlinear elements and study nonautonomous systems with oscillation-induced phase transitions between lowand high-dimensional states. The associated nonlinear immunodynamical phenomenon of nonequilibrial destabilization of a malignant tumor is analyzed in terms of the Prigogine-Glansdorff (1971) stability theorem of dynamical systems theory.
Michael Ederer - One of the best experts on this subject based on the ideXlab platform.
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the Glansdorff prigogine stability criterion for biochemical reaction networks
Automatica, 2011Co-Authors: Michael Ederer, Ernst Dieter Gilles, Oliver SawodnyAbstract:Local stability analysis of steady states in mathematical models of biochemical reaction networks is an important tool for systems biology. The second variation of the Gibbs energy around a steady state is a positive definite function and a candidate for a Lyapunov function. A sufficient condition for the local stability is the local negative definiteness of the time derivative of this function. This is expressed by the Glansdorff-Prigogine stability criterion. Previously, the criterion was criticized to be overly conservative and difficult to check. Here, we derive an easily testable form of the criterion for models of biochemical networks. The criterion can be evaluated with incomplete knowledge of the parameters. For ideal mass-action kinetics, it depends only on the steady state fluxes. For reaction systems in ideal solutions, the Glansdorff-Prigogine criterion is overly conservative and we give a tighter criterion that depends on the same subset of the parameters as the Glansdorff-Prigogine criterion. Whenever these criteria are indefinite, there exist parameter values such that the steady state is unstable. By means of simple example systems we explore these aspects and discuss the possible uses of the criteria for systems biology.