Bifurcation and chaos analysis of tumor growth

In this paper, a dynamic model given by three-dimensional ordinary differential equations is studied to determine how the dynamics of tumor growth is controlled by some key parameters. By varying the competition coefficient between healthy host cells and tumor cells, a Hopf bifurcation occurs in this system, leading to the creation of a stable limit cycle. Through numerical analysis of the continuity of this limit cycle, we find that the cascade of period-doubling bifurcations leads to the generation of a chaotic attractor. Moreover, the region of attractors is shown in the parameter space. Numerical simulations, bifurcation diagrams, Lyapunov exponent graph and phase portraits permit to highlight the rich and complex phenomena presented by the model.