Two-dimensional quadratic nonlinear systems : univariate vector fields / / Albert C. J. Luo

• Autore: Luo Albert C. J.
• Pubblicazione: Singapore : , : Springer, , [2023]; ©2023
• Edizione: 1st ed. 2023.
• Descrizione fisica: 1 online resource (XIII, 685 p. 121 illus., 84 illus. in color.)
• Disciplina: 929.605
• Soggetto topico: Computational complexity
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Two-Dimensional Quadratic Nonlinear Systems
• ISBN: 981-16-7873-1
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910717418003321
• Lo trovi qui: Univ. Federico II
• Serie: Nonlinear Physical Science, . 1867-8459