The resonant center problem for a 2:-3 resonant cubic lotka–volterra system

Jaume Giné; Colin Christopher; Mateja Prešern; Valery G. Romanovski; Natalie L. Shcheglova

doi:10.1007/978-3-642-32973-9_11

The resonant center problem for a 2:-3 resonant cubic lotka–volterra system

Jaume Giné, Colin Christopher, Mateja Prešern, Valery G. Romanovski, Natalie L. Shcheglova

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

14 Citations (Scopus)

Abstract

Using tools of computer algebra we derive the conditions for the cubic Lotka–Volterra system ẋ = x(2 − a₂₀x² − a₁₁xy − a₀₂y²), ẏ = y(−3+b₂₀x² + b₁₁xy + b₀₂y²) to be linearizable and to admit a first integral of the form Φ(x, y) =x³y² + ··· in a neighborhood of the origin, in which case the origin is called a 2: −3 resonant center.

Original language	English
Title of host publication	Computer Algebra in Scientific Computing. CASC 2012
Editors	Vladimir P. Gerdt, Wolfram Koepf, Ernst W. Mayr, Evgenii V. Vorozhtsov
Publisher	Springer
Pages	129-142
Number of pages	14
ISBN (Electronic)	9783642329739
ISBN (Print)	9783642329722
DOIs	https://doi.org/10.1007/978-3-642-32973-9_11
Publication status	Published - 2012
Event	14th International Workshop on Computer Algebra in Scientific Computing 2012 - Maribor, Slovenia Duration: 3 Sept 2012 → 6 Sept 2012

Publication series

Name	Lecture Notes in Computer Science
Volume	7442
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	14th International Workshop on Computer Algebra in Scientific Computing 2012
Abbreviated title	CASC 2012
Country/Territory	Slovenia
City	Maribor
Period	3/09/12 → 6/09/12

Keywords

First integral
Polynomial systems of differential equations
Resonant center problem

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-642-32973-9_11

Cite this

Giné, J., Christopher, C., Prešern, M., Romanovski, V. G., & Shcheglova, N. L. (2012). The resonant center problem for a 2:-3 resonant cubic lotka–volterra system. In V. P. Gerdt, W. Koepf, E. W. Mayr, & E. V. Vorozhtsov (Eds.), Computer Algebra in Scientific Computing. CASC 2012 (pp. 129-142). (Lecture Notes in Computer Science; Vol. 7442). Springer. https://doi.org/10.1007/978-3-642-32973-9_11

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title = "The resonant center problem for a 2:-3 resonant cubic lotka–volterra system",

abstract = "Using tools of computer algebra we derive the conditions for the cubic Lotka–Volterra system ẋ = x(2 − a20x2 − a11xy − a02y2), ẏ = y(−3+b20x2 + b11xy + b02y2) to be linearizable and to admit a first integral of the form Φ(x, y) =x3y2 + ··· in a neighborhood of the origin, in which case the origin is called a 2: −3 resonant center.",

keywords = "First integral, Polynomial systems of differential equations, Resonant center problem",

author = "Jaume Gin{\'e} and Colin Christopher and Mateja Pre{\v s}ern and Romanovski, {Valery G.} and Shcheglova, {Natalie L.}",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2012.; 14th International Workshop on Computer Algebra in Scientific Computing 2012, CASC 2012 ; Conference date: 03-09-2012 Through 06-09-2012",

year = "2012",

doi = "10.1007/978-3-642-32973-9_11",

language = "English",

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series = "Lecture Notes in Computer Science",

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Giné, J, Christopher, C, Prešern, M, Romanovski, VG & Shcheglova, NL 2012, The resonant center problem for a 2:-3 resonant cubic lotka–volterra system. in VP Gerdt, W Koepf, EW Mayr & EV Vorozhtsov (eds), Computer Algebra in Scientific Computing. CASC 2012. Lecture Notes in Computer Science, vol. 7442, Springer, pp. 129-142, 14th International Workshop on Computer Algebra in Scientific Computing 2012, Maribor, Slovenia, 3/09/12. https://doi.org/10.1007/978-3-642-32973-9_11

The resonant center problem for a 2:-3 resonant cubic lotka–volterra system. / Giné, Jaume; Christopher, Colin; Prešern, Mateja et al.
Computer Algebra in Scientific Computing. CASC 2012. ed. / Vladimir P. Gerdt; Wolfram Koepf; Ernst W. Mayr; Evgenii V. Vorozhtsov. Springer, 2012. p. 129-142 (Lecture Notes in Computer Science; Vol. 7442).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AU - Giné, Jaume

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AU - Prešern, Mateja

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AU - Shcheglova, Natalie L.

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N2 - Using tools of computer algebra we derive the conditions for the cubic Lotka–Volterra system ẋ = x(2 − a20x2 − a11xy − a02y2), ẏ = y(−3+b20x2 + b11xy + b02y2) to be linearizable and to admit a first integral of the form Φ(x, y) =x3y2 + ··· in a neighborhood of the origin, in which case the origin is called a 2: −3 resonant center.

AB - Using tools of computer algebra we derive the conditions for the cubic Lotka–Volterra system ẋ = x(2 − a20x2 − a11xy − a02y2), ẏ = y(−3+b20x2 + b11xy + b02y2) to be linearizable and to admit a first integral of the form Φ(x, y) =x3y2 + ··· in a neighborhood of the origin, in which case the origin is called a 2: −3 resonant center.

KW - First integral

KW - Polynomial systems of differential equations

KW - Resonant center problem

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The resonant center problem for a 2:-3 resonant cubic lotka–volterra system

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