Bifurcation and Stability in Nonlinear Dynamical Systems

Albert C. J. Luo (Autor)

Buch | Hardcover

XI, 411 Seiten

2020 | 1st ed. 2019
Springer International Publishing (Verlag)
978-3-030-22909-2 (ISBN)

Artikel merken

This book systematically presents a fundamental theory for the local analysis of bifurcation and stability of equilibriums in nonlinear dynamical systems. Until now, one does not have any efficient way to investigate stability and bifurcation of dynamical systems with higher-order singularity equilibriums. For instance, infinite-equilibrium dynamical systems have higher-order singularity, which dramatically changes dynamical behaviors and possesses the similar characteristics of discontinuous dynamical systems. The stability and bifurcation of equilibriums on the specific eigenvector are presented, and the spiral stability and Hopf bifurcation of equilibriums in nonlinear systems are presented through the Fourier series transformation. The bifurcation and stability of higher-order singularity equilibriums are presented through the (2m)th and (2m+1)th -degree polynomial systems. From local analysis, dynamics of infinite-equilibrium systems is discussed. The research on infinite-equilibrium systems will bring us to the new era of dynamical systems and control.

Presents an efficient way to investigate stability and bifurcation of dynamical systems with higher-order singularity equilibriums;
Discusses dynamics of infinite-equilibrium systems;
Demonstrates higher-order singularity.

Dr. Albert C. J. Luo is Distinguished Research Professor in the Department of Mechanical Engineering, Southern Illinois University Edwardsville, Edwardsville, IL.

Stability of equilibriums.- Bifurcation of equilibriums.- Low-dimensional dynamical system.- Equilibrium and higher-singularity.- Low-degree polynomial systems.- (2m)th-degree polynomial systems.- (2m+1)th-degree polynomial systems.- Infinite-equilibrium systems.

"The book should be of interest to research and practising scientists and engineers as well as Ph.D. students in the field of nonlinear dynamical systems and control theory." (Clementina Mladenova, zbMATH 1440.93005, 2020)

Erscheinungsdatum	01.02.2020
Reihe/Serie	Nonlinear Systems and Complexity
Zusatzinfo	XI, 411 p. 78 illus., 64 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	982 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Technik ► Maschinenbau
Schlagworte	Complexity • higher-order singularity • Hopf Bifurcation • infinite-equilibrium systems • local stability and bifurcations • nonlinear dynamical systems • Ordinary differential equations • Partial differential equations
ISBN-10	3-030-22909-2 / 3030229092
ISBN-13	978-3-030-22909-2 / 9783030229092
Zustand	Neuware