Chaotic dynamics of a cancer model with singular and non-singular kernel
Hardik Joshi, Mehmet Yavuz
Abstract
In this paper, the chaos and chaotic dynamics of cancer cells are studied by using singular and non-singular kernel operators. A deterministic cancer model is considered that shows the interaction between normal cells, tumor cells, and effectors immune cells. The analysis, existence, and uniqueness of the cancer model are derived for singular and non-singular kernel operators by using fixed point and Picard–Lindelof criteria. The numerical solution of the cancer model is provided for singular and non-singular kernel operators. The time series and phase space evolution of the different cells is obtained to examine the periodic, chaotic behavior under the influence of various biological situations. The numerical result highlights the substantial role of model parameters, singular, and non-singular kernels in the transmission dynamics of cancer cells.