Phase Portraits of Planar Quadratic Systems

1. Auflage. Softcover version of original hardcover Auflage 2007
ISBN: 978-1-4419-4024-7
Verlag: Springer US

Buch, Englisch, Band 583, 334 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 534 g

Reihe: Mathematics and Its Applications

Although some examples of phase portraits of quadratic systems can already be found in the work of Poincaré, the first paper dealing exclusively with these systems was published by Büchel in 1904. By the end of the 20th century an increasing flow of publications resulted in nearly a thousand papers on the subject.

This book attempts to give a presentation of the advance of our knowledge of phase portraits of quadratic systems, paying special attention to the historical development of the subject. The book organizes the portraits into classes, using the notions of finite and infinite multiplicity and finite and infinite index. Classifications of phase portraits for various classes are given using the well-known methods of phase plane analysis.

Zielgruppe

Research

Autoren/Hrsg.

Reyn, John

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Naturwissenschaften Biowissenschaften Biowissenschaften
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Critical points in quadratic systems.- Isoclines, critical points and classes of quadratic systems.- Analyzing phase portraits of quadratic systems.- Phase portraits of quadratic systems in the class mf=0.- Quadratic systems with center points.- Limit cycles in quadratic systems.- Phase portraits of quadratic systems in the class mf=1.- Phase portraits of quadratic systems in the class mf=2.- Phase portraits of quadratic systems in the class mf=3.- Phase portraits of quadratic systems in the class mf=4.