NDLI: How to estimate the number of limit cycles in Lienard systems with a small parameter

Content Provider	Springer Nature Link
Author	Cherkas, L. A. Malysheva, O. N.
Copyright Year	2011
Abstract	To estimate the number of limit cycles and locate them for polynomial Lienard systems with a small parameter in the case of a perturbation of a center and in the case of the existence of relaxation limit cycles, we develop a method for constructing a modified Dulac function in the form of a series in the small parameter.In the case of a perturbation of a center for Lienard systems, we suggest an heuristic method for the approximation of limit cycles appearing from the closed phase curves surrounding the center; in this method, we use the ovals obtained by equating the leading term in the expansion of the reciprocal of the integrating factor in powers of the small parameter with zero.The suggested method for finding Dulac functions permits one to single out one-parameter families of Lienard systems that have a constant (independent of the parameter) number of limit cycles. We present examples of such systems.
Starting Page	224
Ending Page	230
Page Count	7
File Format	PDF
ISSN	00122661
Journal	Differential Equations
Volume Number	47
Issue Number	2
e-ISSN	16083083
Language	English
Publisher	SP MAIK Nauka/Interperiodica
Publisher Date	2011-04-08
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Difference and Functional Equations Ordinary Differential Equations Partial Differential Equations
Content Type	Text
Resource Type	Article
Subject	Analysis

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

How to estimate the number of limit cycles in Lienard systems with a small parameter