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Palabras claves o descriptores: CONTINUATION (Comienzo)
2 registros cumplieron la condición especificada en la base de información BIBCYT. ()
Registro 1 de 2, Base de información BIBCYT
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Kuznetsov, Yu. A. ; De Feo, O. ; Rinaldi, S.
Título: Belyakov Homoclinic Bifurcations in a Tritrophic Food Chain Model
Páginas/Colación: pp. 462-487
Url: Ir a http://siamdl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SMJMAP000062000002000462000001&idtype=cvips&gifs=Yeshttp://siamdl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SMJMAP000062000002000462000001&idtype=cvips&gifs=Yes
SIAM Journal on Applied Mathematics Vol. 62, no. 2 Oct./Dec. 2001
Información de existenciaInformación de existencia

Palabras Claves: Palabras: CONTINUATION CONTINUATION, Palabras: HOMOCLINIC BIFURCATIONS HOMOCLINIC BIFURCATIONS, Palabras: POPULATION DYNAMICS POPULATION DYNAMICS

Resumen
RESUMEN

RESUMEN

Complex dynamics of the most frequently used tritrophic food chain model are investigated in this paper. First it is shown that the model admits a sequence of pairs of Belyakov bifurcations (codimension-two homoclinic orbits to a critical node). Then fold and period-doubling cycle bifurcation curves associated to each pair of Belyakov points are computed and analyzed. The overall bifurcation scenario explains why stable limit cycles and strange attractors with different geometries can coexist. The analysis is conducted by combining numerical continuation techniques with theoretical arguments.

Registro 2 de 2, Base de información BIBCYT
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Doedel, E. J. ; Govaerts, W. ; Kuznetsov, Yu. A.
Título: Computation of Periodic Solution Bifurcations in ODEs Using Bordered Systems
Páginas/Colación: pp. 401 - 435
Url: Ir a http://epubs.siam.org/sam-bin/dbq/article/40077http://epubs.siam.org/sam-bin/dbq/article/40077
Siam Journal on Numerical Analysis Vol. 41, no. 2 April-May 2004
Información de existenciaInformación de existencia

Palabras Claves: Palabras: BIFURCATIONS BIFURCATIONS, Palabras: BOUNDARY VALUE PROBLEMS BOUNDARY VALUE PROBLEMS, Palabras: CONTINUATION CONTINUATION, Palabras: PERIODIC SOLUTIONS PERIODIC SOLUTIONS

Resumen
We consider numerical methods for the computation and continuation of the three generic secondary periodic solution bifurcations in autonomous ODEs, namely the fold, the period-doubling (or flip) bifurcation, and the torus (or Neimark--Sacker) bifurcation. In the fold and flip cases we append one scalar equation to the standard periodic BVP that defines the periodic solution; in the torus case four scalar equations are appended. Evaluation of these scalar equations and their derivatives requires the solution of linear BVPs, whose sparsity structure (after discretization) is identical to that of the linearization of the periodic BVP. Therefore the calculations can be done using existing numerical linear algebra techniques, such as those implemented in the software AUTO and COLSYS.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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