Control and numerical analysis for cancer chaotic system

Abstract

This article investigates the problem of control of chaotic dynamics of tumor cells, immune system cells, and healthy tissue cells in a three-dimensional cancer model by adaptive control technique. Adaptive control law is derived such that the trajectory of controlled system asymptotically approaches equilibrium point with estimated parameter converges to stabilizing values. A nonlinear control law is designed which change the original chaotic system into a controlled one linear system. In addition, we present and analyze numerical solution of the cancer dynamical system with the help of a discretization technique. Achieved solutions show a comparable results with Runge–Kutta methods. The reliability and accuracy of the proposed technique is presented by comparing numerical results. The used technique has displayed a brilliant prospective in dealing with the numerical solutions of nonlinear dynamical systems.