Abstract
This study deals with the control of chaotic dynamics of tumor cells, healthy host cells, and effector immune cells in a chaotic Three Dimensional Cancer Model (TDCM) by State Space Exact Linearization (SSEL) technique based on Lie algebra. A non-linear feedback control law is designed which induces a coordinate transformation thereby changing the original chaotic TDCM system into a controlled one linear system. Numerical simulation has been carried using Mathematica that witness the robustness of the technique implemented on the chosen chaotic system.
Highlights
Cancer pertains to a class of diseases characterized by out-of-control cell growth
We have controlled the chaotic dynamics of Three Dimensional Cancer Model (TDCM) using the State Space Exact Linearization (SSEL) method based on Lie algebra
SSEL method based on system has been obtained using
Summary
Cancer pertains to a class of diseases characterized by out-of-control cell growth. Unsatisfactory performance of immune system against cancerous abnormal cells and their chaotic growth leads to serious health damages and even death. De Pillis and Radunskaya [2] included a normal tissue cell population in this model, performed phase space analysis, and investigated the effect of chemotherapy treatment by using optimal control theory whereas Kirschner and Panetta [3] examined the cancer cell growth in the presence of the effector immune cells and the cytokine IL-2 which has an essential role in the activation and stimulation of the immune system. They implied that antigenicity of the cancer cells plays an essential role in the recognition of cancer cells by the immune system.
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