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Bifurcation and Stability in Nonlinear Dynamical Systems

  • Albert C. J. Luo
Book

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. Albert C. J. Luo
    Pages 1-57
  3. Albert C. J. Luo
    Pages 59-85
  4. Albert C. J. Luo
    Pages 87-122
  5. Albert C. J. Luo
    Pages 123-148
  6. Albert C. J. Luo
    Pages 149-229
  7. Albert C. J. Luo
    Pages 231-288
  8. Albert C. J. Luo
    Pages 289-363
  9. Albert C. J. Luo
    Pages 365-408
  10. Back Matter
    Pages 409-411

About this book

Introduction

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.

Keywords

nonlinear dynamical systems higher-order singularity hopf bifurcation infinite-equilibrium systems local stability and bifurcations

Authors and affiliations

  • Albert C. J. Luo
    • 1
  1. 1.Southern Illinois UniversityEdwardsvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-22910-8
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-22909-2
  • Online ISBN 978-3-030-22910-8
  • Series Print ISSN 2195-9994
  • Series Online ISSN 2196-0003
  • Buy this book on publisher's site