NDLI: Singularly perturbed Hopf bifurcation

Content Provider	IEEE Xplore Digital Library
Author	Abed, E.
Copyright Year	1974
Description	Hopf bifurcation is the simplest way in which periodic solutions can emerge from an equilibrium point of an autonomous one-parameter family of ordinary differential equations. The phenomenon occurs if the linearized system has a pair of complex-conjugate simple eigenvalues which cross the imaginary axis transversely for some value of the parameter. In this paper, conditions are derived which ensure persistence of the Hopf bifurcation under singular perturbations of the vector field. The results justify use of reduced-order models in the study of nonlinear oscillations via Hopf bifurcation. Both single parameter and multiparameter singular perturbation problems are considered. In the single parameter case, we show how Fenichel's center manifold theorem for singularly perturbed systems can be used to prove regular degeneration of the bifurcated periodic solutions and to study their stability. In the multiparameter case, we obtain a novel asymptotic formula for the eigenvalues of the perturbed system. This formula is valid regardless of the relative magnitudes of the small parameters, and the results on multiparameter singularly perturbed Hopf bifurcation apply to two time scales as well as multiple time-scale systems.
Starting Page	1270
Ending Page	1280
Page Count	11
File Size	1340365
File Format	PDF
ISSN	00984094
Volume Number	32
Issue Number	12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1985-12-01
Publisher Place	U.S.A.
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Bifurcation Eigenvalues and eigenfunctions Stability Fluid dynamics Differential equations Reduced order systems Chemicals Power system dynamics Active circuits Books
Content Type	Text
Resource Type	Article
Subject	Engineering

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Initial conditions for reduced-order models of nonlinear singularly perturbed systems

Bifurcation Analysis on Power System Voltage Stability

Analysis of voltage control systems exhibiting Hopf bifurcation

The effects of generation redispatch on Hopf bifurcations in electric power systems

Sliding mode control for singularly perturbed system

Exponential Stability of Singularly Perturbed Systems

On Hopf bifurcations in singularly perturbed systems

On Bifurcations of Power Systems at Singularities

Dynamic equivalents by combination of reduced order models of system components

Singularly perturbed Hopf bifurcation

Similar Documents

Initial conditions for reduced-order models of nonlinear singularly perturbed systems

Bifurcation Analysis on Power System Voltage Stability

Analysis of voltage control systems exhibiting Hopf bifurcation

The effects of generation redispatch on Hopf bifurcations in electric power systems

Sliding mode control for singularly perturbed system

Exponential Stability of Singularly Perturbed Systems

On Hopf bifurcations in singularly perturbed systems

On Bifurcations of Power Systems at Singularities

Dynamic equivalents by combination of reduced order models of system components

Singularly perturbed Hopf bifurcation