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Chaos in Dissipativen Systemen

Chaos in Dissipativen Systemen

          
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About the Book

Dynamische Systeme konnen durch mathematische Gleichungen modelliert werden, die eine eindeutige V orschrift zur Berechnung der zeitlichen Entwicklung des Systemzustandes darstellen, so daB die Bewegung des Systems vollstandig durch den Anfangs- zustand bestimmt ist. Trotz dieser Determiniertheit stellt sich bei der numerischen Berechnung der Losungskurven oder bei Beob- achtungen in realen Experimenten haufig hera us, daB sich der Zustand des Systems in au Berst komplizierter und unregelmaBiger Weise mit der Zeit andert und daB eng benachbarte Startbedin- gungen nach endlicher Zeit zu vollig unterschiedlichen Zustanden fiihren konnen. Man spricht dann von chaotischen Bewegungen bzw. nennt das betreffende System chaotisch. In den letzten 10 bis 15 Jahren sind betrachtliche Fortschritte im Verstandnis der Dynamik nichtlinearer deterministischer Systeme gemacht worden. Das Konzept des chaotischen (oder seltsamen) Attraktors, verbunden mit den Vorstellungen von fraktaler Dimension, Entropie und universellen Bifurkations- sequenzen auf dem Wege zum Chaos, hat zu einem neuen Denken beziiglich dieser Systeme gefiihrt. Dabei ist u. a. auch klar gewor- den, daB Chaos nicht einfach mit Unordnung oder Regellosigkeit gleichgesetzt werden kann. An die Stelle von Gleichformigkeit .oder Periodizitat treten andere Ordnungsbegriffe, die eng mit Selbstahnlichkeit, Skaleninvarianz und Universalitat verbunden sind. Einen wesentlichen Beitrag zu diesem neuen Verstandnis hat die moderne Rechentechnik geleistet. Da Chaos untrennbar mit Nichtlinearitat verbunden ist, deren mathematische Behandlung sich in den meisten Fallen als auBerordentlich schwierig erweist, konnten viele interessante Fragestellungen und teilweise sehr all- gemeine GesetzmaBigkeiten chaotischer Bewegungen erst auf der Basis ausgedehnter numerischer Berechnungen formuliert bzw.


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Product Details
  • ISBN-13: 9783528063566
  • Publisher: Vieweg+teubner Verlag
  • Publisher Imprint: Vieweg+teubner Verlag
  • Height: 203 mm
  • No of Pages: 189
  • Series Title: German
  • Weight: 195 gr
  • ISBN-10: 3528063564
  • Publisher Date: 01 Jan 1989
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Spine Width: 10 mm
  • Width: 127 mm


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