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Nonnegative Periodic Solutions of a Three-Term Recurrence Relation Depending on Two Real Parameters
Joint Authors
Chang, Yen Chih
Cheng, Sui Sun
Yeh, Wei Chang
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-21, 21 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-09-06
Country of Publication
Egypt
No. of Pages
21
Main Subjects
Abstract EN
Simple dynamic systems representing time varying states of interconnected neurons may exhibit extremely complex behaviors when bifurcation parameters are switched from one set of values to another.
In this paper, motivated by simulation results, we examine the steady states of one such system with bang-bang control and two real parameters.
We found that nonnegative and negative periodic states are of special interests since these states are solutions of linear nonhomogeneous three-term recurrence relations.
Although the standard approach to analyse such recurrence relations is the method of finding the general solutions by means of variation of parameters, we find novel alternate geometric methods that offer the tracking of solution trajectories in the plane.
By means of this geometric approach, we are then able, without much tedious computation, to completely characterize the nonnegative and negative periodic solutions in terms of the bifurcation parameters.
American Psychological Association (APA)
Chang, Yen Chih& Cheng, Sui Sun& Yeh, Wei Chang. 2017. Nonnegative Periodic Solutions of a Three-Term Recurrence Relation Depending on Two Real Parameters. Discrete Dynamics in Nature and Society،Vol. 2017, no. 2017, pp.1-21.
https://search.emarefa.net/detail/BIM-1151702
Modern Language Association (MLA)
Chang, Yen Chih…[et al.]. Nonnegative Periodic Solutions of a Three-Term Recurrence Relation Depending on Two Real Parameters. Discrete Dynamics in Nature and Society No. 2017 (2017), pp.1-21.
https://search.emarefa.net/detail/BIM-1151702
American Medical Association (AMA)
Chang, Yen Chih& Cheng, Sui Sun& Yeh, Wei Chang. Nonnegative Periodic Solutions of a Three-Term Recurrence Relation Depending on Two Real Parameters. Discrete Dynamics in Nature and Society. 2017. Vol. 2017, no. 2017, pp.1-21.
https://search.emarefa.net/detail/BIM-1151702
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1151702