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

被引：1
|
作者：
Drexler, Daniel Andras [1 ]
Nagy, Ilona [2 ,6 ]
Romanovski, Valery G. [3 ,4 ,5 ]
机构：
[1] Obuda Univ, Physiol Controls Res Ctr, Budapest, Hungary
[2] Budapest Univ Technol & Econ, Inst Math, Dept Anal & Operat Res, Budapest, Hungary
[3] Univ Maribor, Fac Elect Engn & Comp Sci, Maribor, Slovenia
[4] Univ Maribor, Ctr Appl Math & Theoret Phys, Maribor, Slovenia
[5] Univ Maribor, Fac Nat Sci & Math, Maribor, Slovenia
[6] Budapest Univ Technol & Econ, Inst Math, Dept Anal & Operat Res, Muegyetem Rkp 3, H-1111 Budapest, Hungary
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2024年 / 47卷 / 07期
基金：
欧盟地平线“2020”;
关键词：
bifurcation; cancer therapy; limit cycle; singular point; tumor control; tumor therapy;
D O I：
10.1002/mma.9885
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：5677 / 5691
页数：15
相关论文
共 50 条
  • [31] BISTABILITY, GENERALIZED AND ZERO-HOPF BIFURCATIONS IN A PEST CONTROL MODEL WITH FARMING AWARENESS
    AL Basir, Fahad
    Samanta, Sudip
    Tiwari, Pankaj Kumar
    JOURNAL OF BIOLOGICAL SYSTEMS, 2023, 31 (01) : 115 - 140
  • [32] Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network
    Zhao, Wen-bo
    Sun, Xiao-ke
    Wang, Huicheng
    ABSTRACT AND APPLIED ANALYSIS, 2014,
  • [33] Stability and Hopf Bifurcation Analysis for an Age-Structured Tumor Immune Model with Time Delay
    Luo, Zhonghu
    Liu, Zijian
    Tan, Yuanshun
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2023, 33 (07):
  • [34] Stability and Hopf bifurcation analysis in DCTCP congestion control
    Cheng Zunshui
    Jiang Jingna
    Sun Dongsheng
    The Journal of China Universities of Posts and Telecommunications, 2023, 30 (06) : 30 - 37
  • [35] Stability and hopf bifurcation analysis in DCTCP congestion control
    Zunshui C.
    Jingna J.
    Dongsheng S.
    Journal of China Universities of Posts and Telecommunications, 2023, 30 (06): : 30 - 37and59
  • [36] Stability analysis of traveling wave fronts in a model for tumor growth
    Swartwood, Brea
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2025, 81
  • [37] Numerical stability analysis and computation of Hopf bifurcation points for delay differential equations
    Luzyanina, T
    Roose, D
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1996, 72 (02) : 379 - 392
  • [38] ON THE STABILITY OF NUMERICAL-METHODS OF HOPF POINTS USING BACKWARD ERROR ANALYSIS
    REDDIEN, GW
    COMPUTING, 1995, 55 (02) : 163 - 180
  • [39] Stability and Hopf bifurcation analysis in a TCP fluid model
    Liu, Feng
    Guan, Zhi-Hong
    Wang, Hua O.
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2011, 12 (01) : 353 - 363
  • [40] Stability and Hopf Bifurcation Analysis of a Delayed SEIS Model
    Reddy, Madhusudhan K.
    Narayan, Lakshmi K.
    Reddy, Ravindra B.
    INTERNATIONAL JOURNAL OF ECOLOGY & DEVELOPMENT, 2021, 36 (01) : 82 - 90
12345