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One‐parametric families of canard cycles: two explicitly solvable examples
Author(s) -
Schneider Klaus R.,
Shchetinina Ekaterina V.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310023
Subject(s) - limit cycle , limit (mathematics) , amplitude , integrable system , mathematics , bifurcation , parametric statistics , plane (geometry) , ordinary differential equation , mathematical analysis , infinite period bifurcation , differential equation , hopf bifurcation , nonlinear system , physics , geometry , quantum mechanics , statistics
Systems of singularly perturbed autonomous ordinary differential equations possessing in a parameter plane two intersecting bifurcation curves connected with the generation of limit cycles with large and small amplitude respectively, have a special class of limit cycles called canards or french ducks describing an exponentially fast transition from a small amplitude limit cycle to limit cycle with a large amplitude. We present two explicitly integrable examples of non‐autonomous singularly perturbed di.erential equations with canard cycles without a second parameter.