Necessary conditions for the existence of quasi-polynomial invariants: the quasi-polynomial and Lotka–Volterra systems

A. Figueiredo, T.M.Rocha Filho and L. Brenig

Physica A: Statistical Mechanics and its Applications, 1999, vol. 262, issue 1, 158-180

Abstract: We show that any quasi-polynomial invariant of a quasi-polynomial dynamical system can be transformed into a quasi-polynomial invariant of a homogeneous quadratic Lotka–Volterra dynamical system. We show how this quasi-polynomial invariant can be decomposed in a simple manner. This decomposition permits to conclude that the existence of polynomial semi-invariants in Lotka–Volterra systems is a necessary condition for the existence of quasi-polynomial invariants. We derive a method which allows to construct the necessary conditions for existence of semi-invariants on Lotka–Volterra dynamical systems. Applications are given.

Keywords: Dynamical systems; Nonlinear; Invariants; Semi-invariants; Lotka–Volterra (search for similar items in EconPapers)
Date: 1999
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437198003963
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:262:y:1999:i:1:p:158-180

DOI: 10.1016/S0378-4371(98)00396-3

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().