Integrability and global dynamics of the May–Leonard model

Blé, Gamaliel; Castellanos, Víctor; Llibre, Jaume; Quilantán, Ingrid

doi:10.1016/j.nonrwa.2012.06.004

Cited by 18 publications

(27 citation statements)

References 23 publications

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“…In this section, using the Elimination Theorem, we look for Darboux polynomials of degree two for system (4). A general form of a polynomial of degree two is…”

Section: Darboux Polynomials Of System (4)mentioning

confidence: 99%

“…x + y + z = 1, all orbits inside the triangle are closed and every orbit in the interior of R 3 + has one of these closed orbits as an ω-limit. Latter on, the dynamics of Equation (2) was studied in more details in [4][5][6] and some other works.…”

Section: Introductionmentioning

confidence: 99%

“…The dynamics of Equation 4were studied in [6][7][8][9]. In particular, Chi, Hsu and Wu [8] studied (4) under the assumption 0…”

Section: Introductionmentioning

confidence: 99%

“…It was shown in [4] that system (2) is completely integrable, that is, it admits two independent first integrals, if either α + β = 2 or β = α.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we study integrability of the asymmetric May-Leonard model (4). Using algorithms from elimination theory, we first find systems of the form in Equation (4) admitting invariant planes and invariant surfaces defined by the quadratic polynomials.…”

Section: Introductionmentioning

confidence: 99%

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First Integrals of the May–Leonard Asymmetric System

et al. 2019

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“…In this section, using the Elimination Theorem, we look for Darboux polynomials of degree two for system (4). A general form of a polynomial of degree two is…”

Section: Darboux Polynomials Of System (4)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The dynamics of Equation 4were studied in [6][7][8][9]. In particular, Chi, Hsu and Wu [8] studied (4) under the assumption 0…”

Section: Introductionmentioning

confidence: 99%

“…It was shown in [4] that system (2) is completely integrable, that is, it admits two independent first integrals, if either α + β = 2 or β = α.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

First Integrals of the May–Leonard Asymmetric System

et al. 2019

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The Completely Integrable Differential Systems are Essentially Linear Differential Systems

2015

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Abstract. Letẋ = f (x) be a C k autonomous differential system with k ∈ N ∪ {∞, ω} defined in an open subset Ω of R n . Assume that the systemẋ = f (x) is C r completely integrable, i.e. there exist n − 1 functionally independent first integrals of class C r with 2 ≤ r ≤ k. If the divergence of systemẋ = f (x) is non-identically zero, then any Jacobian multiplier is functionally independent of the n − 1 first integrals. Moreover the systemẋ = f (x) is C r−1 orbitally equivalent to the linear differential systemẏ = y in a full Lebesgue measure subset of Ω. For Darboux and polynomial integrable polynomial differential systems we characterize their type of Jacobian multipliers.

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