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luo two dimensional quadratic nonlinear systems vol 1 vector fields 2023

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Textbook in PDF format 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. Two-Dimensional Linear Dynamical Systems Single-Variable Quadratic Systems with a Self-Univariate Quadratic Vector Field Single-Variable Quadratic Systems with a Non-Self-Univariate Quadratic Vector Field Variable-Independent Quadratic Dynamics Variable-Crossing Univariate Quadratic Systems Two-Univariate Product Quadratic Systems Product-Bivariate Quadratic Systems with a Self-Univariate Quadratic Vector Field Product-Bivariate Quadratic Systems with a Non-Self-Univariate Quadratic Vector Field

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Luo A. Nonlinear Vibration Reduction...Tuned Mass Damper System 2022.pdf 5.2 MB
Luo A. Two-Dimensional Quadratic Nonlinear Systems. Vol 1...Vector Fields 2023.pdf 8.5 MB

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luo two dimensional quadratic nonlinear systems vol 1 vector fields 2023