Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Versal deformation and static bifurcation diagrams for the cancer cell population model


Authors: Vladimir Balan and Ileana Rodica Nicola
Journal: Quart. Appl. Math. 67 (2009), 755-770
MSC (2000): Primary 37G10, 37G35, 70K50
DOI: https://doi.org/10.1090/S0033-569X-09-01169-X
Published electronically: May 14, 2009
MathSciNet review: 2588235
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Abstract | References | Similar Articles | Additional Information

Abstract: The paper studies the existence of rest-points and the static bifurcation diagrams of a given nonlinear differential system modeling the cancer cell population evolution from biology. To this aim, the nullclines, the equilibrium points, the transient set, the static bifurcation equation and the associated versal deformation are investigated. The results are further discussed in view of potential applications to cancer therapy.


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Additional Information

Vladimir Balan
Affiliation: University “Politehnica” of Bucharest, Faculty of Applied Sciences, Dept. Mathematics-Informatics I, Splaiul Indpendentei 313, RO-060042 Bucharest, Romania
Email: vbalan@mathem.pub.ro

Ileana Rodica Nicola
Affiliation: University “Spiru Haret” of Bucharest, Faculty of Mathematics and Informatics, Ion Ghica Str. 13, RO-030045 Bucharest, Romania
Email: nicola_rodica@yahoo.com

DOI: https://doi.org/10.1090/S0033-569X-09-01169-X
Keywords: Static bifurcation diagram, versal deformation, transient set, hysteresis set, nullclines, normal form, quiescent cell population, proliferating cell population
Received by editor(s): August 25, 2008
Published electronically: May 14, 2009
Article copyright: © Copyright 2009 Brown University
The copyright for this article reverts to public domain 28 years after publication.


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