Skip to main content
SpringerLink
Log in
Book cover

Bifurcation and Stability in Nonlinear Dynamical Systems

  • Book
  • © 2019

Overview

Authors:
  1. Albert C. J. Luo

    1. Southern Illinois University, Edwardsville, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • 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

Part of the book series: Nonlinear Systems and Complexity (NSCH, volume 28)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 69.99 USD 129.00
46% discount Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 89.99 USD 169.99
47% discount Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 89.99 USD 169.99
47% discount Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (8 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Stability of Equilibriums

    • Albert C. J. Luo
    Pages 1-57

  3. Bifurcations of Equilibrium

    • Albert C. J. Luo
    Pages 59-85

  4. Low-Dimensional Dynamical Systems

    • Albert C. J. Luo
    Pages 87-122

  5. Equilibrium Stability in 1-Dimensional Systems

    • Albert C. J. Luo
    Pages 123-148

  6. Low-Degree Polynomial Systems

    • Albert C. J. Luo
    Pages 149-229

  7. (2m)th-Degree Polynomial Systems

    • Albert C. J. Luo
    Pages 231-288

  8. (2m+1)th-Degree Polynomial Systems

    • Albert C. J. Luo
    Pages 289-363

  9. Infinite-Equilibrium Systems

    • Albert C. J. Luo
    Pages 365-408

  10. Back Matter

    Pages 409-411
    Download chapter PDF
Back to top

Keywords

About this book

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.


Reviews

“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)

Authors and Affiliations

  • Southern Illinois University, Edwardsville, USA

    Albert C. J. Luo

About the author

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

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation