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A Discrete Dynamics Approach to a Tumor System

Author

Listed:
  • Tareq Saeed

    (Nonlinear Analysis and Applied Mathematics (NAAM)—Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Kamel Djeddi

    (Laboratory of Dynamical Systems and Control, Department of Mathematics and Computer Science, Larbi Ben MHidi University, Oum El Bouaghi 4000, Algeria)

  • Juan L. G. Guirao

    (Nonlinear Analysis and Applied Mathematics (NAAM)—Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
    Departamento de Matemáca Aplicada y Estadística, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain)

  • Hamed H. Alsulami

    (Nonlinear Analysis and Applied Mathematics (NAAM)—Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Mohammed Sh. Alhodaly

    (Nonlinear Analysis and Applied Mathematics (NAAM)—Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

Abstract

In this paper, we present a cancer system in a continuous state as well as some numerical results. We present discretization methods, e.g., the Euler method, the Taylor series expansion method, and the Runge–Kutta method, and apply them to the cancer system. We studied the stability of the fixed points in the discrete cancer system using the new version of Marotto’s theorem at a fixed point; we prove that the discrete cancer system is chaotic. Finally, we present numerical simulations, e.g., Lyapunov exponents and bifurcations diagrams.

Suggested Citation

  • Tareq Saeed & Kamel Djeddi & Juan L. G. Guirao & Hamed H. Alsulami & Mohammed Sh. Alhodaly, 2022. "A Discrete Dynamics Approach to a Tumor System," Mathematics, MDPI, vol. 10(10), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1774-:d:821849
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