Stability Analysis of the Steady-State Solution of a Mathematical Model in Tumor Angiogenesis

Pamuk, Serdal

doi:10.1063/1.1814752

Cited by 2 publications

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“…Similarly, in [4,6] the authors consider the Turing-Hopf bifurcation arising from the reaction-diffusion equations, and in [3,5] the authors derive a necessary and sufficient condition for Turing instabilities to occur in two-component systems of reaction-diffusion equations with Neumann boundary conditions. In [7] the authors study the stability analysis of the steady-state solution of a mathematical model in tumor angiogenesis whereas in [10] Hopf bifurcation of a ratio -dependent predator-prey model involving two discrete maturation time delays is considered.…”

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confidence: 99%

Stability and Hopf Bifurcation Analysis of a Mathematical Model in Tumor Angiogenesis

Pamuk¹,

Çay²

2018

ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY a - Applied Sciences and Engineering

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This work has been presented at the "International Conference on Mathematics and Engineering, 10-12 May, 2017, Istanbul, Turkey". In this paper we introduce a stability and Hopf bifurcation analysis of a reaction diffusion system which models the interaction between endothelial cells and the inhibitor. Then, we investigate the stability of the positive equilibrium solutions under some conditions. We also show the existence of a Hopf bifurcation and provide some figures to show that the equilibrium solutions are indeed asymptotically stable.

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