### 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 language | English |
---|---|

Pages (from-to) | 3129-3134 |

Number of pages | 6 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 376 |

Issue number | 45 |

DOIs | |

Publication status | Published - Oct 1 2012 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**The underlying linear dynamics of some positive polynomial systems.** / Hangos, K.; Szederkényi, G.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - The underlying linear dynamics of some positive polynomial systems

AU - Hangos, K.

AU - Szederkényi, G.

PY - 2012/10/1

Y1 - 2012/10/1

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

UR - http://www.scopus.com/inward/record.url?scp=84868145833&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84868145833&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2012.10.004

DO - 10.1016/j.physleta.2012.10.004

M3 - Article

AN - SCOPUS:84868145833

VL - 376

SP - 3129

EP - 3134

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 45

ER -