Phase Portraits of Planar Quadratic Systems

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.

List of contents

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.

Summary

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.

Product details

• Authors: John Reyn
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 14.04.2009
• EAN: 9780387304137
• ISBN: 978-0-387-30413-7
• No. of pages: 334
• Weight: 676 g
• Illustrations: XVI, 334 p. 144 illus.
• Series: Mathematics and Its Applications; Mathematics and Its Applicatio; Mathematics and Its Applications; Mathematics and Its Applicatio
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Analysis, B, Dynamics, Mathematics and Statistics, Genetics and Population Dynamics, Ordinary Differential Equations, Dynamical Systems and Ergodic Theory, Ergodic theory, Nonlinear science, Differential equations, Dynamical systems, Applied mathematics, Biomathematics, Population Genetics, DEX;Finite;classification;development;knowledge;presentation