Phase Portraits of Planar Quadratic Systems [electronic resource] /
Reyn, John.author.
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.
Description based upon print version of record.
Includes bibliographical references (p. 307-332) and index.
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.
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.
Differential Equations.
Differentiable dynamical systems.
Genetics
Ordinary Differential Equations.
Dynamical Systems and Ergodic Theory.
Genetics and Population Dynamics.
Mathematics and its applications