A Fractional Order Tumor Growth Model and Its Synchronization.

This paper introduces a new model of a tumor growth biological system. Based on fractional-order calculus, the proposed model presents intricate chaotic dynamics as the fractional derivatives are swept even if it preserves the same equilibrium points as the integer order version. In particular, numerical simulations of chaotic attractors and bifurcation diagrams are used to evidence the three phases of tumor growth, i.e., avascular, vascular, and metastasis. After that, a control technique is designed to drive the response system from a chaotic phase to a periodic state. The synchronization conditions were attained by using a proper Lyapunov function to control the behavior of the response system. Finally, numerical results agree well with our theoretical findings showing the usefulness of the proposed model