The underlying linear dynamics of some positive polynomial systems

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Abstract

The conditions of structural dynamical similarity of two special classes of positive polynomial nonlinear systems, the class of quasi-polynomial systems (Brenig (1988) [1]) and that of reaction kinetic networks with mass action kinetics (Horn and Jackson (1972) [2]) are investigated in this Letter. It is shown that both system classes have an underlying reduced linear dynamics. By applying the theory of X-factorable systems (Samardzija et al. (1989) [9]), it can be shown that the reduced linear dynamics is qualitatively similar to the original one within the positive orthant when the original nonlinear system has a unique positive equilibrium point.

Original languageEnglish
Pages (from-to)3129-3134
Number of pages6
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume376
Issue number45
DOIs
Publication statusPublished - Oct 1 2012

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polynomials
nonlinear systems
reaction kinetics
kinetics

Keywords

  • Linear dynamics
  • Mass action law
  • Nonlinear systems
  • Quasi-polynomial systems
  • Reaction kinetic systems

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

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title = "The underlying linear dynamics of some positive polynomial systems",
abstract = "The conditions of structural dynamical similarity of two special classes of positive polynomial nonlinear systems, the class of quasi-polynomial systems (Brenig (1988) [1]) and that of reaction kinetic networks with mass action kinetics (Horn and Jackson (1972) [2]) are investigated in this Letter. It is shown that both system classes have an underlying reduced linear dynamics. By applying the theory of X-factorable systems (Samardzija et al. (1989) [9]), it can be shown that the reduced linear dynamics is qualitatively similar to the original one within the positive orthant when the original nonlinear system has a unique positive equilibrium point.",
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AU - Hangos, K.

AU - Szederkényi, G.

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N2 - The conditions of structural dynamical similarity of two special classes of positive polynomial nonlinear systems, the class of quasi-polynomial systems (Brenig (1988) [1]) and that of reaction kinetic networks with mass action kinetics (Horn and Jackson (1972) [2]) are investigated in this Letter. It is shown that both system classes have an underlying reduced linear dynamics. By applying the theory of X-factorable systems (Samardzija et al. (1989) [9]), it can be shown that the reduced linear dynamics is qualitatively similar to the original one within the positive orthant when the original nonlinear system has a unique positive equilibrium point.

AB - The conditions of structural dynamical similarity of two special classes of positive polynomial nonlinear systems, the class of quasi-polynomial systems (Brenig (1988) [1]) and that of reaction kinetic networks with mass action kinetics (Horn and Jackson (1972) [2]) are investigated in this Letter. It is shown that both system classes have an underlying reduced linear dynamics. By applying the theory of X-factorable systems (Samardzija et al. (1989) [9]), it can be shown that the reduced linear dynamics is qualitatively similar to the original one within the positive orthant when the original nonlinear system has a unique positive equilibrium point.

KW - Linear dynamics

KW - Mass action law

KW - Nonlinear systems

KW - Quasi-polynomial systems

KW - Reaction kinetic systems

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