Hopf point analysis for angiogenesis models
type: Item
instance of: scholarly article
title: Hopf point analysis for angiogenesis models
zbMATH Open document ID: 1051.34059
author: Levon Arakelyan
author: Zvia Agur
author: Peteris Daugulis
author: Yuval Ginosar
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2004-05-27T00:00:00Z
review text: The authors present several ODE systems encoding the most essential observations and assumption on the complex hierarchical interactive processes of tumor neo-vascularization. From experimental results they infer that a significant marker of tumor aggressiveness is the oscillatory behavior of tumor size, which is driven by its vascularization dynamics. To study the forces underlying these oscillations, they perform a Hopf-point analysis of the angiogenesis models and obtain the result that Hopf points appear if and only if a nontrivial set of time-delays is introduced into the tumor proliferation or the neo-vascularization process.
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 37G10
Mathematics Subject Classification ID: 92C50
zbMATH DE Number: 2069698
MaRDI profile type: Publication
full work available at URL: dcdsb.2004.4.29
OpenAlex ID: W2167481327
DOI: 10.3934/DCDSB.2004.4.29
description: scientific article; zbMATH DE number 2069698