HOPF point analysis for angiogenesis models

Z. Agur, L. Arakelyan, P. Daugulis, Y. Ginosar

Research output: Contribution to journalArticlepeer-review


In this paper we present several ODE systems encoding the most essential observations and assumptions about the complex hierarchical interactive processes of tumor neo-vascularization (angiogenesis). From experimental results we 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 we perform a Hopf point analysis of the angiogenesis models. In the analyzed models Hopf points appear if and only if a nontrivial set of time-delays is introduced into the tumor proliferation or the neo-vascularization process. We suggest to examine in laboratory experiments how to employ these results for containing cancer growth.

Original languageEnglish
Pages (from-to)29-38
Number of pages10
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number1
StatePublished - Feb 2004
Externally publishedYes


  • Angiogenesis
  • Hopf points
  • Time-delay differential equations

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


Dive into the research topics of 'HOPF point analysis for angiogenesis models'. Together they form a unique fingerprint.

Cite this