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Two-Dimensional Quadratic Nonlinear Systems

Two-Dimensional Quadratic Nonlinear Systems

Volume I: Univariate Vector Fields

by Albert C. J. Luo
Hardback
Publication Date: 21/04/2023

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This book focuses on the nonlinear dynamics based on the vector fields with univariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems. It provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical systems. Such a two-dimensional dynamical system is one of simplest dynamical systems in nonlinear dynamics, but the local and global structures of equilibriums and flows in such two-dimensional quadratic systems help us understand other nonlinear dynamical systems, which is also a crucial step toward solving the Hilbert's sixteenth problem. Possible singular dynamics of the two-dimensional quadratic systems are discussed in detail. The dynamics of equilibriums and one-dimensional flows in two-dimensional systems are presented. Saddle-sink and saddle-source bifurcations are discussed, and saddle-center bifurcations are presented. The infinite-equilibrium states are switching bifurcations for nonlinear systems. From the first integral manifolds, the saddle-center networks are developed, and the networks of saddles, source, and sink are also presented. This book serves as a reference book on dynamical systems and control for researchers, students, and engineering in mathematics, mechanical, and electrical engineering.

ISBN:
9789811678721
9789811678721
Category:
Statistical physics
Format:
Hardback
Publication Date:
21-04-2023
Language:
English
Publisher:
Springer
Country of origin:
United States
Dimensions (mm):
235x155mm
Weight:
1.21kg

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