Journal
NONLINEARITY
Volume 14, Issue 6, Pages 1473-1491Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0951-7715/14/6/304
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We consider the dynamics of singularly perturbed differential equations near points where the critical manifold has a transcritical or a pitchfork singularity. Our main tool is the recently developed blow-up method, which allows a detailed geometric analysis of such problems. A version of the Melnikov method to study transversality properties in this and related problems is developed.
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