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Antimonotonicity, Crisis, and Route to Chaos in a Tumor Growth Model

Antimonotonicity, Crisis, and Route to Chaos in a Tumor Growth Model
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Author(s): Dionysios Sourailidis (Laboratory of Nonlinear Systems – Circuits and Complexity, Physics Department, Aristotle University of Thessaloniki, Greece), Christos Volos (Laboratory of Nonlinear Systems – Circuits & Complexity, Physics Department, Aristotle University of Thessaloniki, Greece), Lazaros Moysis (Laboratory of Nonlinear Systems – Circuits and Complexity, Physics Department, Aristotle University of Thessaloniki, Greece)and Ioannis Stouboulos (Laboratory of Nonlinear Systems – Circuits and Complexity, Physics Department, Aristotle University of Thessaloniki, Greece)
Copyright: 2021
Pages: 14
Source title: Handbook of Research on Modeling, Analysis, and Control of Complex Systems
Source Author(s)/Editor(s): Ahmad Taher Azar (Faculty of Computers and Artificial Intelligence, Benha University, Benha, Egypt & College of Computer and Information Sciences, Prince Sultan University, Riyadh, Saudi Arabia)and Nashwa Ahmad Kamal (Faculty of Engineering, Cairo University, Giza, Egypt)
DOI: 10.4018/978-1-7998-5788-4.ch023

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Abstract

In this chapter, a new model of a tumor growth is dynamically investigated. The model is presented in a form of a system of three ordinary differential equations, which describe the avascular, vascular, and metastasis tumor growth, respectively. For the investigation of system's dynamics and especially of the population of the immune cells in system's behavior, some of the most well-known tools from nonlinear theory, such as the phase portrait, the Poincaré map, the bifurcation diagram the Kaplan-Yorke dimension, and the Lyapunov exponents have been used. Interesting phenomena related with chaos theory, such as a period-doubling route to chaos, crisis phenomena, and antimonotonicity, have been revealed for the first time in this model.

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