Stability analysis of the singular points and Hopf bifurcations of a tumor growth control model

Author:

Drexler Dániel András1,Nagy Ilona2ORCID,Romanovski Valery G.345

Affiliation:

1. Physiological Controls Research Center Óbuda University Budapest Hungary

2. Department of Analysis and Operations Research Institute of Mathematics, Budapest University of Technology and Economics Budapest Hungary

3. Faculty of Electrical Engineering and Computer Science University of Maribor Maribor Slovenia

4. Center for Applied Mathematics and Theoretical Physics University of Maribor Maribor Slovenia

5. Faculty of Natural Science and Mathematics University of Maribor Maribor Slovenia

Abstract

We carry out qualitative analysis of a fourth‐order tumor growth control model using ordinary differential equations. We show that the system has one positive equilibrium point, and its stability is independent of the feedback gain. Using a Lyapunov function method, we prove that there exist realistic parameter values for which the systems admit limit cycle oscillations due to a supercritical Hopf bifurcation. The time evolution of the state variables is also represented.

Funder

Javna Agencija za Raziskovalno Dejavnost RS

Al-Farabi Kazakh National University

Publisher

Wiley

Subject

General Engineering,General Mathematics

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