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Title: Singular Hopf bifurcation in systems with fast and slow variables
Authors: BRAAKSMA, Barteld
Issue Date: 1998
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,
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ISI #: 000075452900001
Type: Journal Contribution
Validations: ecoom 1999
Appears in Collections:Research publications

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