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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. --- Equations, Quadratic. --- 517.91 Differential equations --- Differential equations --- Quadratic equations --- Differential Equations. --- Differentiable dynamical systems. --- Genetics --- Ordinary Differential Equations. --- Dynamical Systems and Ergodic Theory. --- Genetics and Population Dynamics. --- Mathematics. --- Biology --- Embryology --- Mendel's law --- Adaptation (Biology) --- Breeding --- Chromosomes --- Heredity --- Mutation (Biology) --- Variation (Biology) --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics

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