Please use this identifier to cite or link to this item:
|Title:||Singular Hopf bifurcation in systems with fast and slow variables||Authors:||BRAAKSMA, Barteld||Issue Date:||1998||Publisher:||SPRINGER VERLAG||Source:||JOURNAL OF NONLINEAR SCIENCE, 8(5). p. 457-490||Abstract:||We study a general nonlinear ODE system with fast and slow variables, i.e., some of the derivatives are multiplied by a small parameter. The system depends on an additional bifurcation parameter. We derive a normal form for this system, valid close to equilibria where certain conditions on the derivatives hold. The most important condition concerns the presence of eigenvalues with singular imaginary parts, by which we mean that their imaginary part grows without bound as the small parameter tends to zero. We give a simple criterion to test for the possible presence of equilibria satisfying this condition. Using a center manifold reduction, we show the existence of Hopf bifurcation points, originating from the interaction of fast and slow variables, and we determine their nature. We apply the theory, developed here, to two examples: an extended Bonhoeffer-van der Pol system and a predator-prey model. Our theory is in good agreement with the numerical continuation experiments we carried out for the examples.||Notes:||Limburgs Univ Ctr, B-3590 Diepenbeek, Belgium.Braaksma, B, Limburgs Univ Ctr, Univ Campus, B-3590 Diepenbeek, Belgium.email@example.com||Document URI:||http://hdl.handle.net/1942/3155||ISI #:||000075452900001||Type:||Journal Contribution||Validations:||ecoom 1999|
|Appears in Collections:||Research publications|
Show full item record
WEB OF SCIENCETM
checked on May 22, 2022
checked on May 26, 2022
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.