Analytic first integrals of the Halphen system

2006 ◽  
Vol 56 (7) ◽  
pp. 1192-1197 ◽  
Author(s):  
Clàudia Valls
Keyword(s):  
First Integrals ◽  
Analytic First Integrals ◽  
Halphen System

scholarly journals On the Integrability of a Tritrophic Food Chain Model

2010 ◽  
Vol 10 (2) ◽  
Author(s):  
Jaume Llibre ◽  
Clàudia Valls
Keyword(s):  
Food Chain ◽  
Formal Series ◽  
Complete Characterization ◽  
First Integrals ◽  
Chain Model ◽  
Darboux Polynomials ◽  
Analytic First Integrals ◽  
Exponential Factors ◽  
Food Chain Model

AbstractIn this paper we work with a vastly analyzed tritrophic food chain model. We provide a complete characterization of their Darboux polynomials and of their exponential factors. We also show the non-existence of polynomial first integrals, of rational first integrals, of local analytic first integrals in a neighborhood of the origin, of first integrals that can be described by formal series and of Darboux first integrals.

On the Global Analytic Integrability of the Belousov–Zhabotinskii System

2008 ◽  
Vol 8 (4) ◽  
Author(s):  
Jaume Llibre ◽  
Clàudia Valls
Keyword(s):  
First Integrals ◽  
Analytic Integrability ◽  
Analytic First Integrals

AbstractThe well-known Belousov-Zhabotinskii system can be written asẋ = s(x + y - qxwith f, q, s, w ∈ ℝ and s ≠ 0. In this paper we characterize its global analytic first integrals.

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