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Periodic solutions bifurcating from a curve of singularity of the jerk system
Author
Source
ZANCO Journal of Pure and Applied Sciences
Issue
Vol. 32, Issue 2 (30 Apr. 2020), pp.55-61, 7 p.
Publisher
Salahaddin University-Erbil Department of Scientific Publications
Publication Date
2020-04-30
Country of Publication
Iraq
No. of Pages
7
Main Subjects
Abstract EN
We investigate a periodic solution which bifurcates from a curve of the singularity of the jerk system in .More precisely, we give the explicit states for the existence of a periodic solution of the jerk system with a nonisolated singular point, where for each singular point has a simple pair of purely imaginary and one zero eigenvalues.
We recall for this point of singularity as a zero- Hopf (z-H) singular point.
The coefficients in the jerk system are described for which the z-H singularity occur at each point of that curve of singularity.
We show that for each point at that curve of singularity there is only one family of parameters which exhibits such type of singular points.
The method of averaging in the second order is utilized to determine one periodic solution which bifurcates from any point of that curve of singularity.
As far as, we realize that this investigation is the study on bifurcations from a curve of nonisolated z-H singularity to provide a periodic solution via the method of averaging.
Under a generic small perturbation at the parameters, we prove that a periodic solution will be bifurcated at any point that located on a curve of a singularity of the jerk system.
American Psychological Association (APA)
Husayn, Niazy H.. 2020. Periodic solutions bifurcating from a curve of singularity of the jerk system. ZANCO Journal of Pure and Applied Sciences،Vol. 32, no. 2, pp.55-61.
https://search.emarefa.net/detail/BIM-1385890
Modern Language Association (MLA)
Husayn, Niazy H.. Periodic solutions bifurcating from a curve of singularity of the jerk system. ZANCO Journal of Pure and Applied Sciences Vol. 32, no. 2 (2020), pp.55-61.
https://search.emarefa.net/detail/BIM-1385890
American Medical Association (AMA)
Husayn, Niazy H.. Periodic solutions bifurcating from a curve of singularity of the jerk system. ZANCO Journal of Pure and Applied Sciences. 2020. Vol. 32, no. 2, pp.55-61.
https://search.emarefa.net/detail/BIM-1385890
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 61
Record ID
BIM-1385890