Universitat de Lleida
    • English
    • català
    • español
  • English 
    • English
    • català
    • español
  • Login
Repositori Obert UdL
View Item 
  •   Home
  • Recerca
  • Matemàtica
  • Articles publicats (Matemàtica)
  • View Item
  •   Home
  • Recerca
  • Matemàtica
  • Articles publicats (Matemàtica)
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Integrability conditions for Lotka–Volterra planar complex quintic systems

Thumbnail
View/Open
016125.pdf (279.2Kb)
Sol·licita una còpia
Issue date
2010
Author
Giné, Jaume
Romanovski, Valery G.
Suggested citation
Giné, Jaume; Romanovski, Valery G.; . (2010) . Integrability conditions for Lotka–Volterra planar complex quintic systems. Nonlinear Analysis: Real World Applications, 2010, vol. 11, núm. 3, p. 2100-2105. https://doi.org/10.1016/j.nonrwa.2009.06.002.
Impact


Web of Science logo    citations in Web of Science

Scopus logo    citations in Scopus

Google Scholar logo  Google Scholar
Share
Export to Mendeley
Metadata
Show full item record
Abstract
In this paper we obtain necessary and sufficient integrability conditions at the origin for the Lotka–Volterra complex quintic systems which are linear systems perturbed by fifth degree homogeneous polynomials, i.e., we consider systems of the form View the MathML sourceẋ=x(1−a40x4−a31x3y−a22x2y2−a13xy3−a04y4), View the MathML sourceẏ=−y(1−b40x4−b31x3y−b22x2y2−b13xy3−b04y4). The necessity of these conditions is derived from the first nine focus-saddle quantities and their sufficiency is proved by finding an inverse integrating factor or a first integral.
URI
http://hdl.handle.net/10459.1/58671
DOI
https://doi.org/10.1016/j.nonrwa.2009.06.002
Is part of
Nonlinear Analysis: Real World Applications, 2010, vol. 11, núm. 3, p. 2100-2105
European research projects
Collections
  • Articles publicats (Matemàtica) [263]
  • Publicacions de projectes de recerca del Plan Nacional [2170]

Related items

Showing items related by title, author, creator and subject.

  • Polynomial and rational first integrals for planar quasi-homogeneous polynomial differential systems 

    Giné, Jaume; Grau Montaña, Maite; Llibre, Jaume (American Institute of Mathematical Sciences, 2013-10)
    In this paper we find necessary and sufficient conditions in order that a planar quasi-homogeneous polynomial differential system has a polynomial or a rational first integral. We also prove that any planar quasi-homogeneous ...
  • Integrability of complex planar systems with homogeneous nonlinearities 

    Fercec, Brigita; Giné, Jaume; Romanovski, Valery G.; Edneral, Victor F. (Elsevier, 2016)
    In this paper we obtain sufficient conditions for the existence of a local analytic first integral for a family of quintic systems having homogeneous nonlinearities. The family studied in this work is the largest one ...
  • Integrability of planar polynomial differential systems through linear differential equations 

    Giacomini, Héctor; Giné, Jaume; Grau Montaña, Maite (Rocky Mountain Mathematics Consortium, 2006)
    In this work we consider rational ordinary differential equations dy/dx = Q(x, y)/P(x, y), with Q(x, y) and P(x, y) coprime polynomials with real coefficients. We give a method to construct equations of this type for ...

Contact Us | Send Feedback | Legal Notice
© 2021 BiD. Universitat de Lleida
Metadata subjected to 
 

 

Browse

All of the repositoryCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

Statistics

View Usage Statistics

D'interès

Política institucional d'accés obertDiposita les teves publicacionsDiposita dades de recercaSuport a la recerca

Contact Us | Send Feedback | Legal Notice
© 2021 BiD. Universitat de Lleida
Metadata subjected to