Description
| Summary: | In this book, the ``canard phenomenon'' occurring in Van der Pol's equation $\epsilon \ddot x+(x^2+x)\dot x+x-a=0$ is studied. For sufficiently small $\epsilon > 0$ and for decreasing $a$, the limit cycle created in a Hopf bifurcation at $a = 0$ stays of ``small size'' for a while before it very rapidly changes to ``big size'', representing the typical relaxation oscillation. The authors give a geometric explanation and proof of this phenomenon using foliations by center manifolds and blow-up of unfoldings as essential techniques. The method is general enough to be useful in the study of other singular perturbation problems.
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| Item Description: | "May 1996, Volume 121, number 577 (first of 4 numbers)." |
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| Physical Description: | ix, 100 p. : ill. ; 26 cm. |
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| Bibliography: | Includes bibliographical references (p. 95-96). |
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| ISBN: | 082180443X |
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