Chaos in a Tumor Growth Model with Delayed Responses of the Immune System
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-04-18
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
A simple prey-predator-type model for the growth of tumor with discrete time delay in the immune system is considered.
It is assumed that the resting and hunting cells make the immune system.
The present model modifies the model of El-Gohary (2008) in that it allows delay effects in the growth process of the hunting cells.
Qualitative and numerical analyses for the stability of equilibriums of the model are presented.
Length of the time delay that preserves stability is given.
It is found that small delays guarantee stability at the equilibrium level (stable focus) but the delays greater than a critical value may produce periodic solutions through Hopf bifurcation and larger delays may even lead to chaotic attractors.
Implications of these results are discussed.
American Psychological Association (APA)
Saleem, M.& Agrawal, Tanuja. 2012. Chaos in a Tumor Growth Model with Delayed Responses of the Immune System. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-16.
https://search.emarefa.net/detail/BIM-993806
Modern Language Association (MLA)
Saleem, M.& Agrawal, Tanuja. Chaos in a Tumor Growth Model with Delayed Responses of the Immune System. Journal of Applied Mathematics No. 2012 (2012), pp.1-16.
https://search.emarefa.net/detail/BIM-993806
American Medical Association (AMA)
Saleem, M.& Agrawal, Tanuja. Chaos in a Tumor Growth Model with Delayed Responses of the Immune System. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-16.
https://search.emarefa.net/detail/BIM-993806
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993806