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.
Audience
This book is intended for mathematics graduate students and researchers studying quadratic systems.
Author(s): John Reyn (auth.)
Series: Mathematics and Its Applications 583
Edition: 1
Publisher: Springer US
Year: 2007
Language: English
Pages: 334
City: New York
Tags: Ordinary Differential Equations; Dynamical Systems and Ergodic Theory; Genetics and Population Dynamics
Front Matter....Pages i-xvi
Introduction....Pages 1-7
Critical points in quadratic systems....Pages 9-29
Isoclines, critical points and classes of quadratic systems....Pages 31-96
Analyzing phase portraits of quadratic systems....Pages 97-108
Phase portraits of quadratic systems in the class m f =0....Pages 109-119
Quadratic systems with center points....Pages 121-146
Limit cycles in quadratic systems....Pages 147-186
Phase portraits of quadratic systems in the class m f =1....Pages 187-204
Phase portraits of quadratic systems in the class m f =2....Pages 205-257
Phase portraits of quadratic systems in the class m f =3....Pages 259-275
Phase portraits of quadratic systems in the class m f =4....Pages 277-304
Back Matter....Pages 305-334
