A Discrete Dynamics Approach to a Tumor System

Abstract

In this paper, we present a cancer system in a continuous state as well as some numerical results. We present discretization methods, e.g., the Euler method, the Taylor series expansion method, and the Runge–Kutta method, and apply them to the cancer system. We studied the stability of the fixed points in the discrete cancer system using the new version of Marotto’s theorem at a fixed point; we prove that the discrete cancer system is chaotic. Finally, we present numerical simulations, e.g., Lyapunov exponents and bifurcations diagrams.

Keywords

• cancer system
• discretization methods
• stability
• chaos
• Lyapunov exponents
• bifurcation