Analysis and Simulation of Chaotic Systems

Frank C. Hoppensteadt

ISBN 10: 0387989439 / ISBN 13: 9780387989433

Verlag: Springer, Berlin, Springer New York, Springer, 2000

Beschreibung

Neuware - Beginning with realistic mathematical or verbal models of physical or biological phenomena, the author derives tractable mathematical models that are amenable to further mathematical analysis or to elucidating computer simulations. For the most part, derivations are based on perturbation methods. Because of this, the majority of the text is devoted to careful derivations of implicit function theorems, the method of averaging, and quasi-static state approximation methods. The duality between stability and perturbation is developed and used, relying heavily on the concept of stability under persistent disturbances. This explains why stability results developed for quite simple problems are often useful for more complicated, even chaotic, ones. Relevant topics about linear systems, nonlinear oscillations, and stability methods for difference, differential-delay, integro- differential and ordinary and partial differential equations are developed throughout the book. For the second edition, the author has restructured the chapters, placing special emphasis on introductory materials in Chapters 1 and 2 as distinct from presentation materials in Chapters 3 through 8. In addition, more material on bifurcations from the point of view of canonical models, sections on randomly perturbed systems, and several new computer simulations have been added.

Bestandsnummer des Verkäufers 9780387989433

Bibliografische Details

• Titel: Analysis and Simulation of Chaotic Systems
• Verlag: Springer, Berlin, Springer New York, Springer
• Erscheinungsjahr: 2000
• Sprache: Englisch
• ISBN-10: 0387989439
• ISBN-13: 9780387989433
• Einband: Buch
• Auflage: 2. Auflage
• Zustand: Neu

Über diesen Titel

Inhaltsangabe

Beginning with realistic mathematical or verbal models of physical or biological phenomena, the author derives tractable models for further mathematical analysis or computer simulations. For the most part, derivations are based on perturbation methods, and the majority of the text is devoted to careful derivations of implicit function theorems, the method of averaging, and quasi-static state approximation methods. The duality between stability and perturbation is developed and used, relying heavily on the concept of stability under persistent disturbances. Relevant topics about linear systems, nonlinear oscillations, and stability methods for difference, differential-delay, integro-differential and ordinary and partial differential equations are developed throughout the book. For the second edition, the author has restructured the chapters, placing special emphasis on introductory materials in Chapters 1 and 2 as distinct from presentation materials in Chapters 3 through 8. In addition, more material on bifurcations from the point of view of canonical models, sections on randomly perturbed systems, and several new computer simulations have been added.