03373nam 2200481 450 991071741800332120230801215441.0981-16-7873-110.1007/978-981-16-7873-8(CKB)5580000000532038(DE-He213)978-981-16-7873-8(MiAaPQ)EBC7240880(Au-PeEL)EBL7240880(PPN)26965657X(EXLCZ)99558000000053203820230801d2023 uy 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierTwo-dimensional quadratic nonlinear systems univariate vector fields /Albert C. J. Luo1st ed. 2023.Singapore :Springer,[2023]©20231 online resource (XIII, 685 p. 121 illus., 84 illus. in color.) Nonlinear Physical Science,1867-8459981-16-7872-3 Includes bibliographical references and index.Chapter 1 Two-dimensional Linear Dynamical Systems -- Chapter 2 Single-variable Quadratic Systems with a Self-univariate Quadratic Vector Field -- Chapter 3 Single-variable Quadratic Systems with a Non-self-univariate Quadratic Vector Field -- Chapter 4 Variable-independent quadratic systems -- Chapter 5 Variable-crossing univariate quadratic systems -- Chapter 6 Two-univariate product quadratic systems -- Chapter 7 Product-bivariate Quadratic Systems with Self-univariate Vector Fields -- Chapter 8 Product-bivariate Quadratic Systems with Non-self-univariate Vector Fields.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.Nonlinear Physical Science,1867-8459Computational complexityComputational complexity.929.605Luo Albert C. J.720985MiAaPQMiAaPQMiAaPQBOOK9910717418003321Two-Dimensional Quadratic Nonlinear Systems2824552UNINA