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2006, ISBN 9780691125893, Volume 9781400840960, xxii, 329
From controlling disease outbreaks to predicting heart attacks, dynamic models are increasingly crucial for understanding biological processes. Many... 
Biology-Mathematical models
Book
SIAM Journal on Applied Dynamical Systems, ISSN 1536-0040, 2008, Volume 7, Issue 4, pp. 1355 - 1377
Hopf bifurcations have been studied intensively in two dimensional vector fields with one slow and one fast variable [E. Benoit et al., Collect. Math., 31... 
MATHEMATICS, APPLIED | singular perturbation | MIXED-MODE OSCILLATIONS | mixed mode oscillation | CANARDS | R-3 | Hopf bifurcation | PHYSICS, MATHEMATICAL | RELAXATION OSCILLATIONS
Journal Article
Nonlinearity, ISSN 0951-7715, 07/2014, Volume 27, Issue 7, pp. R41 - R50
This article is part of a series commemorating the 50th anniversary of Ed Lorenz's seminal paper 'Deterministic nonperiodic flow'. The system he studied has... 
periodic orbit | SDE Mathematics | attractor dimension | dynamical system | MATHEMATICS, APPLIED | SDE | DIMENSION | STRANGE ATTRACTORS | PHYSICS, MATHEMATICAL | Perturbation methods | Chaos theory | Mathematical models | Trajectories | Orbits | Stochasticity | Dynamical systems | Empirical analysis
Journal Article
Chaos: An Interdisciplinary Journal of Nonlinear Science, ISSN 1054-1500, 03/2008, Volume 18, Issue 1, pp. 015108 - 015108-9
Folded nodes occur in generic slow-fast dynamical systems with two slow variables. Open regions of initial conditions flow into a folded node in an open set of... 
MATHEMATICS, APPLIED | SINGULAR PERTURBATION | PHYSICS, MATHEMATICAL | CANARDS
Journal Article
SIAM Journal on Applied Dynamical Systems, ISSN 1536-0040, 2009, Volume 8, Issue 3, pp. 854 - 879
Slow manifolds are important geometric structures in the state spaces of dynamical systems with multiple time scales. This paper introduces an algorithm for... 
Invariant slow manifold | Canard | Collocation method | Singular perturbaton | collocation method | MATHEMATICS, APPLIED | invariant slow manifold | ORBITS | canard | SYSTEMS | singular perturbaton | BOUNDARY-VALUE ODES | MODEL | INVARIANT-MANIFOLDS | PHYSICS, MATHEMATICAL | COLLOCATION SOFTWARE
Journal Article
Journal of the Royal Society Interface, ISSN 1742-5689, 04/2015, Volume 12, Issue 105, pp. 20150075 - 20150075
Journal Article
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, ISSN 1536-0040, 2010, Volume 9, Issue 1, pp. 138 - 153
This paper investigates travelling wave solutions of the FitzHugh-Nagumo equation from the viewpoint of fast-slow dynamical systems. These solutions are... 
MATHEMATICS, APPLIED | singular perturbation | MIXED-MODE OSCILLATIONS | invariant manifolds | MANIFOLDS | homoclinic bifurcation | HOPF | PHYSICS, MATHEMATICAL
Journal Article
Discrete and Continuous Dynamical Systems - Series S, ISSN 1937-1632, 12/2009, Volume 2, Issue 4, pp. 851 - 872
Discrete and Continuous Dynamical Systems - Series S, Vol. 2, No. 4, pp. 851-872, 2009 The FitzHugh-Nagumo equation has been investigated with a wide array of... 
Invariant manifolds | Geometric singular perturbation theory | Homoclinic bifurcation
Journal Article
SIAM Journal on Applied Dynamical Systems, ISSN 1536-0040, 2010, Volume 9, Issue 3, pp. 659 - 703
Journal Article
SIAM Journal on Applied Dynamical Systems, ISSN 1536-0040, 2011, Volume 10, Issue 1, pp. 92 - 128
Journal Article
Journal of the Royal Society Interface, ISSN 1742-5689, 05/2012, Volume 9, Issue 70, pp. 957 - 971
Journal Article