Integrability conditions for Lotka–Volterra planar complex quintic systems
Issue date
2010Suggested 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.
Metadata
Show full item recordAbstract
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.
Is part of
Nonlinear Analysis: Real World Applications, 2010, vol. 11, núm. 3, p. 2100-2105European research projects
Collections
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 ...