On New Fractional-Order Cancer Model: Bifurcations and Chaos

Abstract

In this work, the nonlinear dynamics of the fractional-order cancer tumor growth model are investigated. The stability of the equilibrium points of the proposed fractional system is analyzed by varying both the fractional-order derivatives and one of the system parameters. Moreover, the dynamical behaviors of the models are compared with each other. Numerical simulations are performed to illustrate the analytical results by considering the Caputo fractional derivative and results are reported by means of bifurcation diagrams, computation of the largest Lyapunov exponent, and the phase portraits. The model can explain many biologically observed tumor states and dynamics, such as stable, periodic, and chaotic behaviors in the steady states. Under some conditions, the interactions between tumor cells, healthy host cells, and effector immune cells show that the tumor could become invasive.