QUALITATIVE ANALYSIS OF A MATHEMATICAL MODEL FOR CAPILLARY FORMATION IN TUMOR ANGIOGENESIS
2003 ◽
Vol 13
(01)
◽
pp. 19-33
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Keyword(s):
Qualitative analysis of a mathematical model for capillary formation is presented under assumptions that enzyme and fibronectin concentrations are in quasi-steady state. The aim of this paper is to prove mathematically that the long-time tendency of endothelial cells will be towards the transition probability density function of enzyme and fibronectin. Endothelial cell steady-state solution is obtained and a numerical simulation is provided to show that there is a close agreement between the steady-state solution obtained analytically and the numerically calculated steady-state of the related initial value problem, which provides strong evidence for the stability of this steady-state.
1995 ◽
Vol 38
(2)
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pp. 363-369
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Keyword(s):
2013 ◽
Vol 2013
◽
pp. 1-7
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1964 ◽
Vol 60
(4)
◽
pp. 949-955
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2013 ◽
Vol 24
(4)
◽
pp. 515-564
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Keyword(s):
Bifurcation Analysis in an n-Dimensional Diffusive Competitive Lotka–Volterra System with Time Delay
2015 ◽
Vol 25
(06)
◽
pp. 1550089
1974 ◽
Vol 18
(04)
◽
pp. 224-241
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