Matches in SemOpenAlex for { <https://semopenalex.org/work/W2016191982> ?p ?o ?g. }
Showing items 1 to 86 of
86
with 100 items per page.
- W2016191982 endingPage "1409" @default.
- W2016191982 startingPage "1402" @default.
- W2016191982 abstract "Abstract We consider a quadratic Lienard equation with an unbounded homoclinic loop, which is a solution tending in forward and backward time to a non-hyperbolic equilibrium point located at infinity. Under small time-periodic perturbation, this equilibrium becomes a normally hyperbolic line of singularities at infinity. We show that the perturbed system may present homoclinic bifurcations, leading to the existence of transverse intersections between the stable and unstable manifolds of such a normally hyperbolic line of singularities. The global study concerning the infinity is performed using the Poincare compactification in polar coordinates, from which we obtain a system defined on a set equivalent to a solid torus in R 3 , whose boundary plays the role of the infinity. The transversality of the manifolds is proved using the Melnikov method and implies, via the Birkhoff–Smale Theorem, a complex dynamical behaviour of the perturbed system solutions in the finite part of the phase space. Numerical simulations are performed in order to illustrate this behaviour, which could be called “the chaos arising from infinity”, since it depends on the global structure of the Lienard equation, including the points at infinity. Although applied to a particular case, the analysis presented provides a geometrical approach to study periodic perturbations of homoclinic (or heteroclinic) loops to infinity of any planar polynomial vector field." @default.
- W2016191982 created "2016-06-24" @default.
- W2016191982 creator A5048385249 @default.
- W2016191982 creator A5059877036 @default.
- W2016191982 date "2011-08-01" @default.
- W2016191982 modified "2023-10-01" @default.
- W2016191982 title "Time-periodic perturbation of a Liénard equation with an unbounded homoclinic loop" @default.
- W2016191982 cites W1579026724 @default.
- W2016191982 cites W1986739294 @default.
- W2016191982 cites W2000904793 @default.
- W2016191982 cites W2003029491 @default.
- W2016191982 cites W2007695515 @default.
- W2016191982 cites W2027317202 @default.
- W2016191982 cites W2027347130 @default.
- W2016191982 cites W2033714024 @default.
- W2016191982 cites W2044413922 @default.
- W2016191982 cites W2063827672 @default.
- W2016191982 cites W2067447470 @default.
- W2016191982 cites W2089995439 @default.
- W2016191982 cites W2151077430 @default.
- W2016191982 doi "https://doi.org/10.1016/j.physd.2011.06.006" @default.
- W2016191982 hasPublicationYear "2011" @default.
- W2016191982 type Work @default.
- W2016191982 sameAs 2016191982 @default.
- W2016191982 citedByCount "7" @default.
- W2016191982 countsByYear W20161919822014 @default.
- W2016191982 countsByYear W20161919822015 @default.
- W2016191982 countsByYear W20161919822016 @default.
- W2016191982 countsByYear W20161919822019 @default.
- W2016191982 countsByYear W20161919822023 @default.
- W2016191982 crossrefType "journal-article" @default.
- W2016191982 hasAuthorship W2016191982A5048385249 @default.
- W2016191982 hasAuthorship W2016191982A5059877036 @default.
- W2016191982 hasConcept C114614502 @default.
- W2016191982 hasConcept C121332964 @default.
- W2016191982 hasConcept C134306372 @default.
- W2016191982 hasConcept C155405617 @default.
- W2016191982 hasConcept C158622935 @default.
- W2016191982 hasConcept C177918212 @default.
- W2016191982 hasConcept C181154966 @default.
- W2016191982 hasConcept C184670325 @default.
- W2016191982 hasConcept C186219872 @default.
- W2016191982 hasConcept C200581526 @default.
- W2016191982 hasConcept C2781349735 @default.
- W2016191982 hasConcept C33923547 @default.
- W2016191982 hasConcept C37914503 @default.
- W2016191982 hasConcept C51544822 @default.
- W2016191982 hasConcept C62520636 @default.
- W2016191982 hasConcept C78045399 @default.
- W2016191982 hasConceptScore W2016191982C114614502 @default.
- W2016191982 hasConceptScore W2016191982C121332964 @default.
- W2016191982 hasConceptScore W2016191982C134306372 @default.
- W2016191982 hasConceptScore W2016191982C155405617 @default.
- W2016191982 hasConceptScore W2016191982C158622935 @default.
- W2016191982 hasConceptScore W2016191982C177918212 @default.
- W2016191982 hasConceptScore W2016191982C181154966 @default.
- W2016191982 hasConceptScore W2016191982C184670325 @default.
- W2016191982 hasConceptScore W2016191982C186219872 @default.
- W2016191982 hasConceptScore W2016191982C200581526 @default.
- W2016191982 hasConceptScore W2016191982C2781349735 @default.
- W2016191982 hasConceptScore W2016191982C33923547 @default.
- W2016191982 hasConceptScore W2016191982C37914503 @default.
- W2016191982 hasConceptScore W2016191982C51544822 @default.
- W2016191982 hasConceptScore W2016191982C62520636 @default.
- W2016191982 hasConceptScore W2016191982C78045399 @default.
- W2016191982 hasIssue "17" @default.
- W2016191982 hasLocation W20161919821 @default.
- W2016191982 hasOpenAccess W2016191982 @default.
- W2016191982 hasPrimaryLocation W20161919821 @default.
- W2016191982 hasRelatedWork W1606486778 @default.
- W2016191982 hasRelatedWork W1975991818 @default.
- W2016191982 hasRelatedWork W1979832219 @default.
- W2016191982 hasRelatedWork W2009219077 @default.
- W2016191982 hasRelatedWork W2042172743 @default.
- W2016191982 hasRelatedWork W2055778140 @default.
- W2016191982 hasRelatedWork W2088868073 @default.
- W2016191982 hasRelatedWork W2156504414 @default.
- W2016191982 hasRelatedWork W2288787858 @default.
- W2016191982 hasRelatedWork W2390721418 @default.
- W2016191982 hasVolume "240" @default.
- W2016191982 isParatext "false" @default.
- W2016191982 isRetracted "false" @default.
- W2016191982 magId "2016191982" @default.
- W2016191982 workType "article" @default.