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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Chaos in a Discrete Cancer Model

Journal of Applied Nonlinear Dynamics 11(2) (2022) 297--308 | DOI:10.5890/JAND.2022.06.003

Kenneth Dukuza

University of Pretoria, Department of Mathematics and Applied Mathematics, P/Bag X 20, Pretoria, Republic

of South Africa

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Abstract

In this paper, we construct and analyse a discrete cancer mathematical model. Essential dynamic properties such as positivity and boundedness of solutions are discussed. Using the Lyapunov stability theorem, we prove that one of the tumor-free equilibria is globally asymptotically stable. Furthermore, the discrete model exhibits chaos for certain parameter values and this is supported by the existence of a positive Lyapunov exponent. Numerical simulations are performed to demonstrate our analytical results.

Acknowledgments

The authors acknowledge the University of Pretoria, Department of Mathematics and Applied Mathematics for the provision of research facilities.

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