LEADER 03373nam 2200481 450 001 9910717418003321 005 20230801215441.0 010 $a981-16-7873-1 024 7 $a10.1007/978-981-16-7873-8 035 $a(CKB)5580000000532038 035 $a(DE-He213)978-981-16-7873-8 035 $a(MiAaPQ)EBC7240880 035 $a(Au-PeEL)EBL7240880 035 $a(PPN)26965657X 035 $a(EXLCZ)995580000000532038 100 $a20230801d2023 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTwo-dimensional quadratic nonlinear systems $eunivariate vector fields /$fAlbert C. J. Luo 205 $a1st ed. 2023. 210 1$aSingapore :$cSpringer,$d[2023] 210 4$dİ2023 215 $a1 online resource (XIII, 685 p. 121 illus., 84 illus. in color.) 225 1 $aNonlinear Physical Science,$x1867-8459 311 $a981-16-7872-3 320 $aIncludes bibliographical references and index. 327 $aChapter 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. 330 $aThis book focuses on the nonlinear dynamics based on the vector fields with univariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems. It provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical systems. Such a two-dimensional dynamical system is one of simplest dynamical systems in nonlinear dynamics, but the local and global structures of equilibriums and flows in such two-dimensional quadratic systems help us understand other nonlinear dynamical systems, which is also a crucial step toward solving the Hilbert?s sixteenth problem. Possible singular dynamics of the two-dimensional quadratic systems are discussed in detail. The dynamics of equilibriums and one-dimensional flows in two-dimensional systems are presented. Saddle-sink and saddle-source bifurcations are discussed, and saddle-center bifurcations are presented. The infinite-equilibrium states are switching bifurcations for nonlinear systems. From the first integral manifolds, the saddle-center networks are developed, and the networks of saddles, source, and sink are also presented. This book serves as a reference book on dynamical systems and control for researchers, students, and engineering in mathematics, mechanical, and electrical engineering. 410 0$aNonlinear Physical Science,$x1867-8459 606 $aComputational complexity 615 0$aComputational complexity. 676 $a929.605 700 $aLuo$b Albert C. J.$0720985 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910717418003321 996 $aTwo-Dimensional Quadratic Nonlinear Systems$92824552 997 $aUNINA