Chaos in a discrete cancer model

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Authors

Dukuza, Kenneth

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Publisher

L&H Scientific Publishing

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.

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Keywords

Cancer model, Lyapunov exponents, Lyapunov stability theorem, Nonstandard finite difference method

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Citation

Dukuza, K. 2022, 'Chaos in a discrete cancer model', Journal of Applied Nonlinear Dynamics, vol. 11, no. 2, pp. 297-308, doi : 10.5890/JAND.2022.06.003.