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...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριος συγγραφέας: Reyn, John (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Boston, MA : Springer US, 2007.
Σειρά:Mathematics and Its Applications ; 583
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
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245 1 0 |a Phase Portraits of Planar Quadratic Systems  |h [electronic resource] /  |c by John Reyn. 
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300 |a XVI, 334 p. 144 illus.  |b online resource. 
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490 1 |a Mathematics and Its Applications ;  |v 583 
505 0 |a 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. 
520 |a 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. 
650 0 |a Mathematics. 
650 0 |a Dynamics. 
650 0 |a Ergodic theory. 
650 0 |a Differential equations. 
650 0 |a Biomathematics. 
650 1 4 |a Mathematics. 
650 2 4 |a Ordinary Differential Equations. 
650 2 4 |a Dynamical Systems and Ergodic Theory. 
650 2 4 |a Genetics and Population Dynamics. 
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776 0 8 |i Printed edition:  |z 9780387304137 
830 0 |a Mathematics and Its Applications ;  |v 583 
856 4 0 |u http://dx.doi.org/10.1007/978-0-387-35215-2  |z Full Text via HEAL-Link 
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950 |a Mathematics and Statistics (Springer-11649)