Dynamical Analysis of a Local Lengley-Epstein System Coupled with Fractional Delayed Differential Equations

Ercan Balcı

doi:10.33187/jmsm.1222532

EN

Dynamical Analysis of a Local Lengley-Epstein System Coupled with Fractional Delayed Differential Equations

Abstract

We consider a system of fractional delayed differential equations. The ordinary differential version of the system without delay is introduced in the Lengyel-Epstein reaction-diffusion system. We evaluate the system with and without delay and explore the stability of the unique positive equilibrium. We also prove the existence of Hopf bifurcation for both cases. Furthermore, the impacts of Caputo fractional order parameter and time delay parameter on the dynamics of the system are investigated with numerical simulations. It is also concluded that for different values of time delay parameter, the decreament of the Caputo fractional order parameter has opposite effects on the system in terms of stability.

Keywords

Caputo fractional derivative, Fractional delayed differential equations, Hopf bifurcation, Lengyel-Epstein equation

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Ercan Balcı ^*
0000-0002-8530-7073
Türkiye

Publication Date

August 7, 2023

Submission Date

December 21, 2022

Acceptance Date

April 13, 2023

Published in Issue

Year 2023 Volume: 6 Number: 2

DOI

https://doi.org/10.33187/jmsm.1222532

IZ

https://izlik.org/JA83AX96SL

APA

Balcı, E. (2023). Dynamical Analysis of a Local Lengley-Epstein System Coupled with Fractional Delayed Differential Equations. Journal of Mathematical Sciences and Modelling, 6(2), 56-64. https://doi.org/10.33187/jmsm.1222532

AMA

1.Balcı E. Dynamical Analysis of a Local Lengley-Epstein System Coupled with Fractional Delayed Differential Equations. Journal of Mathematical Sciences and Modelling. 2023;6(2):56-64. doi:10.33187/jmsm.1222532

Chicago

Balcı, Ercan. 2023. “Dynamical Analysis of a Local Lengley-Epstein System Coupled With Fractional Delayed Differential Equations”. Journal of Mathematical Sciences and Modelling 6 (2): 56-64. https://doi.org/10.33187/jmsm.1222532.

EndNote

Balcı E (August 1, 2023) Dynamical Analysis of a Local Lengley-Epstein System Coupled with Fractional Delayed Differential Equations. Journal of Mathematical Sciences and Modelling 6 2 56–64.

IEEE

[1]E. Balcı, “Dynamical Analysis of a Local Lengley-Epstein System Coupled with Fractional Delayed Differential Equations”, Journal of Mathematical Sciences and Modelling, vol. 6, no. 2, pp. 56–64, Aug. 2023, doi: 10.33187/jmsm.1222532.

ISNAD

Balcı, Ercan. “Dynamical Analysis of a Local Lengley-Epstein System Coupled With Fractional Delayed Differential Equations”. Journal of Mathematical Sciences and Modelling 6/2 (August 1, 2023): 56-64. https://doi.org/10.33187/jmsm.1222532.

JAMA

1.Balcı E. Dynamical Analysis of a Local Lengley-Epstein System Coupled with Fractional Delayed Differential Equations. Journal of Mathematical Sciences and Modelling. 2023;6:56–64.

MLA

Balcı, Ercan. “Dynamical Analysis of a Local Lengley-Epstein System Coupled With Fractional Delayed Differential Equations”. Journal of Mathematical Sciences and Modelling, vol. 6, no. 2, Aug. 2023, pp. 56-64, doi:10.33187/jmsm.1222532.

Vancouver

1.Ercan Balcı. Dynamical Analysis of a Local Lengley-Epstein System Coupled with Fractional Delayed Differential Equations. Journal of Mathematical Sciences and Modelling. 2023 Aug. 1;6(2):56-64. doi:10.33187/jmsm.1222532

Cited By

A mathematical modeling of patient-derived lung cancer stem cells with fractional-order derivative

Physica Scripta

https://doi.org/10.1088/1402-4896/ad80e1

29237 Journal of Mathematical Sciences and Modelling 29238

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