Horn, F.J.M. and Jackson, R.: `General mass action kinetics', Arch. Rational Mech. Anal., 1972, 49, pp. 81-116. Home/Search Document Not in Database Summary Related Articles Check |
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Bernstein's 2. theorem and Viro's method for sparse.. - Gatermann, Wolfrum (2003) (Correct)
....on parameters k ij in I K and depending on constants c i . These systems arise when studying the steady states of a di erential system with mass action kinetics modeling chemical reactions. There are many results about these systems in the literature in chemistry and applied mathematics including [HJ72, Cla80, FH77, VH85, Fei95a, Fei95b, HS96, SM00]. In [GH02, Gat01] we started to rephrase the problem in the language of graph theory and to reinterpret known results from the angle of toric geometry [Ful93, Ewa96, Stu96] Instead of abstract toric varieties we are using the Konrad Zuse Zentrum Berlin, Takustr. 7, D 14195 Berlin, Germany or ....
....component and zero otherwise. We denote this matrix by Y and call the polytope generated by its columns Cayleygraph polytope in analogy to the Cayley polytope [GKZ94] The following lemma is an opposite to multistationarity. The content is Theorem 2.16 and Lemma 3. 6 in [SM00] see also [HJ72]. In order to understand the relevant mathematical structure we give an alternative algebraic proof. Lemma 4.5 Assume system (2) and (3) with Y = Y s = Y k and at least one conservation relation. Assume that for certain positive values of the rate constants k ij and c i in the conservation ....
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F. Horn and R. Jackson. General mass action kinetics. Arch. Rat. Mech. Anal., 41:81-116, 1972.
A Parameter-Robust Observer as an Application of ISS Techniques - Chaves (Correct)
....is discussed. A definition of parameter robustness is proposed and an explicit observer for zero deficiency chemical networks is presented, which is robust in this sense. 1 Introduction Consider the following model for chemical reaction networks of Feinberg Horn Jackson zero deficiency type ([3, 4, 5]) with mass action kinetics: x = f A (x) n (b i b j ) 1.1) together with a set of measurements y = h(x) 1.2) The vector x represents the concentration of each species involved in the reactions and thus we will be interested only in those trajectories that evolve in ....
F.J.M. Horn and R. Jackson, "General mass action kinetics", Arch. Rational Mech. Anal., 49, 1972, 81--116.
A Family of Sparse Polynomial Systems Arising in Chemical.. - Gatermann, Huber (1999) (5 citations) (Correct)
....arise in the modeling of chemical reaction systems by the so called mass action kinetics. The polynomials in the system are de ned by two graphs, a weighted directed graph for the chemical reactions and a weighted bipartite graph for the involved chemicals. In the non algebraic chemical literature [4, 11, 12, 13, 14, 17, 23, 28] there have been several attempts to study the number of real positive solutions depending on the structure of the graphs while dynamic phenomena have been studied a lot by numerical mathematicians, see e.g. 7] The investigation of real positive solutions of the sparse polynomial system f(x) 0 ....
F. Horn and R. Jackson. General mass action kinetics. Arch. Rat. Mech. Anal., 41:81-116, 1972.
Structure and Stability of Certain Chemical Networks and.. - Sontag (2001) (2 citations) (Correct)
....the theorems given here will be possible. The class of systems which we consider is, basically, that of deficiency zero chemical reaction networks with mass action kinetics (and one linkage class) in the language of the beautiful and powerful theory developed by Feinberg, Horn, and Jackson, cf. [2, 3, 4, 5, 7]. As a matter of fact, our stability (but not the robustness nor the feedback) results are basically contained in that previous work. The existence and uniqueness of equilibria, and local asymptotic stability, are already proved in the papers by Feinberg, Horn, and Jackson, and we claim no ....
....describe the timeevolution of the concentrations x 1 (t) xn (t) of n given chemical species A 1 ; An . The equations are derived from a consideration of the reactions that are known to occur among the substances A i . Excellent expositions of this material are available, such as [4, 7], so we limit ourselves here to some informal remarks. As an illustration, suppose that each molecule of species A 1 can react with four molecules of A 2 to produce two molecules of A 3 . Reactions involving five molecules are not very realistic, but we wish to illustrate the mathematical ....
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Horn, F.J.M., and Jackson, R., "General mass action kinetics," Arch. Rational Mech. Anal. 49(1972): 81-116.
A Family of Sparse Polynomial Systems Arising in Chemical.. - Gatermann, Huber (1999) (5 citations) (Correct)
....arise in the modelling of chemical reaction systems by the so called mass action kinetics. The polynomials in the system are de ned by two graphs, a weighted directed graph for the chemical reactions and a weighted bipartite graph for the involved chemicals. In the chemical engineering literature [3, 8, 9, 10, 11, 14, 16, 23] there have been several attempts to study the number of real positive solutions depending on the structure of the graphs. The investigation of real positive solutions of the sparse polynomial system f(x) 0 is very important for the application since this are the steady state solutions of a ....
F. Horn and R. Jackson. General mass action kinetics. Arch. Rat. Mech. Anal., 41:81-116, 1972.
State-Estimators for Chemical Reaction Networks of.. - Chaves, Sontag (1 citation) Self-citation (Horn Jackson) (Correct)
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Horn, F.J.M., and Jackson, R., "General mass action kinetics," Arch. Rational Mech. Anal. 49(1972): 81-116. 24
State-Estimators for Chemical Reaction Networks of.. - Chaves, Sontag (2000) (1 citation) Self-citation (Horn Jackson) (Correct)
....of molecules) will lead to a better understanding of cellular dynamical processes. The main objective of this paper is to construct (when and if possible) state observers for the class of systems which describe chemical reaction networks of the type introduced by Feinberg, Horn, and Jackson in [6, 7, 8, 9, 11, 12]. As outputs, we take a subset of state variables or, more generally, monomials in state variables (which could, in practice, be associated to measured reaction rates) We provide here a complete solution to the observer problem for this class. The results given in [20] provide a convenient ....
Horn, F.J.M., and Jackson, R., "General mass action kinetics," Arch. Rational Mech. Anal. 49(1972): 81-116. 37
Some New Directions in Control Theory Inspired by Systems Biology - Sontag (2004) (Correct)
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Horn, F.J.M. and Jackson, R.: `General mass action kinetics', Arch. Rational Mech. Anal., 1972, 49, pp. 81-116.
A Tutorial on Monotone Systems - With an Application to .. - De Leenheer, Angeli.. (2004) (Correct)
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F.J.M. Horn, and R. Jackson, "General mass action kinetics," Archive for Rational Mechanics and Analysis (1972)49:81-116.
Global Behaviour of Polynomial Differential Systems in the.. - Gouze (Correct)
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F. Horn and R. Jackson, General mass action kinetics, Arch. Rational Mech. Anal., 47 (1972) pp. 81-116
Counting Stable Solutions of Sparse Polynomial Systems in.. - Gatermann (2000) (Correct)
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F. Horn, R. Jackson, General Mass Action Kinetics. Arch. Rat. Mech. Anal. 41 (1972), 81-116.
Counting Stable Solutions of Sparse Polynomial Systems in.. - Gatermann (2000) (Correct)
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F. Horn, R. Jackson, General Mass Action Kinetics. Arch. Rat. Mech. Anal. 41 (1972), 81-116.
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