Two-Dimensional Quadratic Nonlinear Systems: Volume I: Univariate Vector Fields

This book discusses the nonlinear dynamics of two-dimensional quadratic systems, focusing on vector fields with univariate quadratic functions. It provides insights into bifurcations, equilibriums, and flows, discussing singular dynamics, saddle-sink and saddle-source bifurcations, and infinite-equilibrium states. It serves as a valuable reference for researchers, students, and engineers in mathematics, mechanical, and electrical engineering.

Format: Hardback
Length: 685 pages
Publication date: 21 April 2023
Publisher: Springer Verlag, Singapore

This comprehensive book delves into the realm of nonlinear dynamics, specifically focusing on systems driven by vector fields with univariate quadratic functions. It stands as a unique monograph dedicated to two-dimensional quadratic nonlinear systems, offering diverse perspectives on nonlinear dynamics and the fascinating phenomena of bifurcations in such systems. While a two-dimensional quadratic dynamical system may be considered one of the simplest in the field of nonlinear dynamics, its local and global structures provide valuable insights into other complex systems. This understanding is a significant step toward solving the renowned Hilbert's sixteenth problem. The book comprehensively explores the potential singular dynamics of two-dimensional quadratic systems, providing detailed discussions. It also presents the dynamics of equilibriums and one-dimensional flows within these systems, shedding light on phenomena such as saddle-sink and saddle-source bifurcations. Furthermore, the book discusses saddle-center bifurcations, infinite-equilibrium states, and the development of saddle-center networks from first integral manifolds. Serving as a valuable reference book for researchers, students, and engineering professionals in mathematics, mechanical, and electrical engineering, this text offers a deep understanding of dynamical systems and control.

Weight: 1208g
Dimension: 235 x 155 (mm)
ISBN-13: 9789811678721
Edition number: 1st ed. 2023