Chaos in a Three-Dimensional Cancer Model with Piecewise Constant Arguments

Senol Kartal

doi:10.17776/csj.1239101

EN

Chaos in a Three-Dimensional Cancer Model with Piecewise Constant Arguments

Abstract

In this study, we analyze a cancer model which includes the interactions among tumor cells, healthy host cells and effector immune cells. The model with continuous case has been studied in the literature and it has been shown that it exhibits chaotic behavior. In this paper, we aim to build a better understanding of how both discrete and continuous times affect the dynamic behavior of the tumor growth model. So, we reconsider the model as a system of differential equations with piecewise constant argument. To analyze dynamical behavior of the model, we consider the solution of the system in a certain subinterval which leads to the system of difference equations. Some theoretical results are obtained for local behavior of the system. In addition, we study chaotic dynamic of the system through Neimark-Sacker bifurcation by using Lyapunov exponents

Keywords

Tumor model, difference equation, stability, Neimark-Sacker bifurcation, Lyapunov exponents

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Senol Kartal ^*
0000-0003-1205-069X
Türkiye

Publication Date

June 30, 2023

Submission Date

January 19, 2023

Acceptance Date

May 1, 2023

Published in Issue

Year 2023 Volume: 44 Number: 2

DOI

https://doi.org/10.17776/csj.1239101

IZ

https://izlik.org/JA88SG69KR

APA

Kartal, S. (2023). Chaos in a Three-Dimensional Cancer Model with Piecewise Constant Arguments. Cumhuriyet Science Journal, 44(2), 345-355. https://doi.org/10.17776/csj.1239101

AMA

1.Kartal S. Chaos in a Three-Dimensional Cancer Model with Piecewise Constant Arguments. CSJ. 2023;44(2):345-355. doi:10.17776/csj.1239101

Chicago

Kartal, Senol. 2023. “Chaos in a Three-Dimensional Cancer Model With Piecewise Constant Arguments”. Cumhuriyet Science Journal 44 (2): 345-55. https://doi.org/10.17776/csj.1239101.

EndNote

Kartal S (June 1, 2023) Chaos in a Three-Dimensional Cancer Model with Piecewise Constant Arguments. Cumhuriyet Science Journal 44 2 345–355.

IEEE

[1]S. Kartal, “Chaos in a Three-Dimensional Cancer Model with Piecewise Constant Arguments”, CSJ, vol. 44, no. 2, pp. 345–355, June 2023, doi: 10.17776/csj.1239101.

ISNAD

Kartal, Senol. “Chaos in a Three-Dimensional Cancer Model With Piecewise Constant Arguments”. Cumhuriyet Science Journal 44/2 (June 1, 2023): 345-355. https://doi.org/10.17776/csj.1239101.

JAMA

1.Kartal S. Chaos in a Three-Dimensional Cancer Model with Piecewise Constant Arguments. CSJ. 2023;44:345–355.

MLA

Kartal, Senol. “Chaos in a Three-Dimensional Cancer Model With Piecewise Constant Arguments”. Cumhuriyet Science Journal, vol. 44, no. 2, June 2023, pp. 345-5, doi:10.17776/csj.1239101.

Vancouver

1.Senol Kartal. Chaos in a Three-Dimensional Cancer Model with Piecewise Constant Arguments. CSJ. 2023 Jun. 1;44(2):345-5. doi:10.17776/csj.1239101

As of 2026, Cumhuriyet Science Journal will be published in six issues per year, released in February, April, June, August, October, and December

Abstract

Keywords

Chaos in a Three-Dimensional Cancer Model with Piecewise Constant Arguments

Abstract

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Acceptance Date

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