Overview
The book is about the global stability and bifurcation of equilibriums in polynomial functional systems. Appearing and switching bifurcations of simple and higher-order equilibriums in the polynomial functional systems are discussed, and such bifurcations of equilibriums are not only for simple equilibriums but for higher-order equilibriums. The third-order sink and source bifurcations for simple equilibriums are presented in the polynomial functional systems. The third-order sink and source switching bifurcations for saddle and nodes are also presented, and the fourth-order upper-saddle and lower-saddle switching and appearing bifurcations are presented for two second-order upper-saddles and two second-order lower-saddles, respectively. In general, the (2𝑙 + 1)th-order sink and source switching bifurcations for (2𝑙𝑖)th-order saddles and (2𝑙𝑗 +1)-order nodes are also presented, and the (2𝑙)th-order upper-saddle and lower-saddle switching and appearing bifurcations are presented for (2𝑙𝑖)th-order upper-saddles and (2𝑙𝑗)th-order lower-saddles (𝑖, 𝑗 = 1,2,…). The vector fields in nonlinear dynamical systems are polynomial functional. Complex dynamical systems can be constructed with polynomial algebraic structures, and the corresponding singularity and motion complexity can be easily determined.
Full Product Details
Author: Albert C. J. Luo
Publisher: Morgan & Claypool Publishers
Imprint: Morgan & Claypool Publishers
ISBN: 9781636392219
ISBN 10: 1636392210
Pages: 165
Publication Date: 30 October 2021
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: In Print
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Author Information
Professor Luo works at Southern Illinois University, Edwardsville. For over 30 years, Dr. Luo's contributions on nonlinear dynamical systems and mechanics lie in (i) the local singularity theory for discontinuous dynamical systems, (ii) dynamical systems synchronization, (iii) analytical solutions of periodic and chaotic motions in nonlinear dynamical systems, (iv) the theory for stochastic and resonant layer in nonlinear Hamiltonian systems, and (v) the full nonlinear theory for a deformable body. Such contributions have been scattered into over 20 monographs and over 300 peer-reviewed journal and conference papers. Dr. Luo served an editor for the journal Communications in Nonlinear Science and Numerical Simulation, book series on Nonlinear Physical Science (HEP), and Nonlinear Systems and Complexity (Springer). Dr. Luo was an editorial member for IMeChE Part K Journal of Multibody Dynamics and the Journal of Vibration and Control, and has organized over 30 international symposiums and conferences on Dynamics and Control.
