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On a Difference Equation with Exponentially Decreasing Nonlinearity
Joint Authors
Saker, Samir H.
Braverman, Elena
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-07-28
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
We establish a necessary and sufficient condition for global stability of the nonlinear discrete red blood cells survival model and demonstrate that local asymptotic stability implies global stability.
Oscillation and solution bounds are investigated.
We also show that, for different values of the parameters, the solution exhibits some time-varying dynamics, that is, if the system is moved in a direction away from stability (by increasing the parameters), then it undergoes a series of bifurcations that leads to increasingly long periodic cycles and finally to deterministic chaos.
We also study the chaotic behavior of the model with a constant positive perturbation and prove that, for large enough values of one of the parameters, the perturbed system is again stable.
American Psychological Association (APA)
Braverman, Elena& Saker, Samir H.. 2011. On a Difference Equation with Exponentially Decreasing Nonlinearity. Discrete Dynamics in Nature and Society،Vol. 2011, no. 2011, pp.1-17.
https://search.emarefa.net/detail/BIM-449556
Modern Language Association (MLA)
Braverman, Elena& Saker, Samir H.. On a Difference Equation with Exponentially Decreasing Nonlinearity. Discrete Dynamics in Nature and Society No. 2011 (2011), pp.1-17.
https://search.emarefa.net/detail/BIM-449556
American Medical Association (AMA)
Braverman, Elena& Saker, Samir H.. On a Difference Equation with Exponentially Decreasing Nonlinearity. Discrete Dynamics in Nature and Society. 2011. Vol. 2011, no. 2011, pp.1-17.
https://search.emarefa.net/detail/BIM-449556
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-449556