Stability analysis of a fractional-order cancer model with chaotic dynamics  

作　　者：Parvaiz Ahmad Naik Jian Zu Mehraj-ud-din Naikt 

机构地区：[1]School of Mathematics and Statistics,Xi’an Jiaotong University Xi’an,Shaanxi 710049,P.R.China [2]Department of Chemical Engineering,College of Engineering Jazan University,Jazan 45142,Saudi Arabia

出　　处：《International Journal of Biomathematics》2021年第6期239-261,共23页生物数学学报（英文版）

基　　金：supported by grants from the China Postdoctoral Science Foundation(Grant Nos.2019M663653 and 2014M560755);the National Natural Science Foundation of China(Grant Nos.11971375,11571272,11201368 and 11631012);the National Science and Technology major project of China(Grant No.2018ZX10721202);grant from the Natural Science Foundation of Shaanxi Province(Grant No.2019JM-273).

摘　　要：In this paper,we develop a three-dimensional fractional-order cancer model.The proposed model involves the interaction among tumor cells,healthy tissue cells and activated effector cells.The detailed analysis of the equilibrium points is studied.Also,the existence and uniqueness of the solution are investigated.The fractional derivative is considered in the Caputo sense.Numerical simulations are performed to illustrate the effectiveness of the obtained theoretical results.The outcome of the study reveals that the order of the fractional derivative has a significant effect on the dynamic process.Further,the calculated Lyapunov exponents give the existence of chaotic behavior of the proposed model.Also,it is observed from the obtained results that decrease in fractional-order p increases the chaotic behavior of the model.

关 键 词：Cancer model Caputo fractional derivative CHAOS stability analysis. 

分 类 号：O17[理学—数学]