Chaos in a discrete cancer model

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.