Bifurcation and stability in nonlinear dynamical systems
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 d…
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- Full title :Bifurcation and stability in nonlinear dynamical systems / Albert C.J. Luo.
Summary
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.
Read More ↓Edition Statements
- Publication Date:2019
Publication Statements
- Publisher(s):Springer
- Place of Publication:Cham, Switzerland
- Language:eng
- Publication Date:2019
The Physical Object
- Description:1 online resource
Edition Identifiers
- ISBN:9783030229108, 3030229106
- DOI:10.1007/978-3-030-22910-8
- oclc:on1139151768
- LC Classification:QA372
- Dewey Decimal:515.352
Table of Contents
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.
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