Oscillators with chaotic behavior: An illustration of a theorem by Shil'nikov
Identifieur interne : 004152 ( Main/Exploration ); précédent : 004151; suivant : 004153Oscillators with chaotic behavior: An illustration of a theorem by Shil'nikov
Auteurs : A. Arneodo [France] ; P. Coullet [France] ; C. Tresser [France]Source :
- Journal of Statistical Physics [ 0022-4715 ] ; 1982-01-01.
Abstract
Abstract: Using an explicit one-parameter family of differential equations describing oscillators with feedback effects, we prove the existence of values of the parameters such that there exist infinitely many unstable periodic orbits of saddle type. The proof relies on a theorem by Shil'nikov which we propose as an explanation for the origin and structure of the chaotic behavior displayed by many well-known third-order differential systems.
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DOI: 10.1007/BF01011745
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The proof relies on a theorem by Shil'nikov which we propose as an explanation for the origin and structure of the chaotic behavior displayed by many well-known third-order differential systems.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Provence-Alpes-Côte d'Azur</li></region><settlement><li>Nice</li></settlement></list><tree><country name="France"><region name="Provence-Alpes-Côte d'Azur"><name sortKey="Arneodo, A" sort="Arneodo, A" uniqKey="Arneodo A" first="A." last="Arneodo">A. Arneodo</name></region><name sortKey="Arneodo, A" sort="Arneodo, A" uniqKey="Arneodo A" first="A." last="Arneodo">A. Arneodo</name><name sortKey="Coullet, P" sort="Coullet, P" uniqKey="Coullet P" first="P." last="Coullet">P. Coullet</name><name sortKey="Coullet, P" sort="Coullet, P" uniqKey="Coullet P" first="P." last="Coullet">P. Coullet</name><name sortKey="Tresser, C" sort="Tresser, C" uniqKey="Tresser C" first="C." last="Tresser">C. 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