A Discrete Dynamics Approach to a Tumor System

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.

Automated summary

In this paper, a continuous state cancer system and various numerical results are presented. Discretization methods, such as the Euler method, Taylor series expansion method, and Runge-Kutta method, are introduced and applied to the cancer system. The stability of fixed points in the discrete cancer system is studied using a modified version of Marotto's theorem, and it is proven that the discrete cancer system exhibits chaos. Numerical simulations, including Lyapunov exponents and bifurcation diagrams, are also presented.