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292089

On the dynamics of a Riccati differential equation with perturbed delay

Article

Last updated: 29 Dec 2024

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Tags

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Abstract

Within the scope of this study, we discuss the new concept of a perturbed delay. As a simple example, we will focus on a Riccati differential equation with a perturbed delay to illustrate this concept. We look at both the solution's existence and its continuous dependence on the initial conditions. Analyses of Hopf bifurcations and the local stability of the fixed points are presented. In order to solve the delay differential equation with piecewise constant arguments, we adopt a discretization procedure. We do an analysis of the local stability of the discrete system. We use numerical simulations to draw out the results, like bifurcation diagrams, Lyapunov exponents, and phase diagrams. This helps us confirm our research and unearth more complex dynamics. We contrast the results of theoretical studies of the delayed Riccati differential equation and its perturbed equation. Our results show that, under certain conditions, the Riccati differential equation with perturbed delay is equivalent to the Riccati differential equation with the same dynamical properties.

DOI

10.21608/ejmaa.2023.192905.1007

Keywords

riccati equation, Perturbed delay, Stability analysis, Bifurcation, Chaos

Authors

First Name

Ahmed M. A.

Last Name

El-Sayed

MiddleName

-

Affiliation

Department of Mathematics, Faculty of Science, Alexandria University, Egypt.

Email

amasayed@alexu.edu.eg

City

-

Orcid

0000-0001-7092-7950

First Name

Sanaa M.

Last Name

Salman

MiddleName

-

Affiliation

Department of Mathematics, Faculty of Education, Alexandria University

Email

samastars9@alexu.edu.eg

City

-

Orcid

0000-0003-4112-394X

First Name

AbdAllah A. F.

Last Name

AbdElfattah

MiddleName

-

Affiliation

Department of Mathematics and computer science, Faculty of Science, Alexandria University

Email

abdallah.awad_pg@alexu.edu.eg

City

-

Orcid

0000-0002-0651-6898

Volume

11

Article Issue

2

Related Issue

39572

Issue Date

2023-07-01

Receive Date

2023-02-13

Publish Date

2023-07-01

Page Start

1

Page End

14

Print ISSN

3009-6731

Online ISSN

2090-729X

Link

https://ejmaa.journals.ekb.eg/article_292089.html

Detail API

https://ejmaa.journals.ekb.eg/service?article_code=292089

Order

292,089

Type

Regular research papers

Type Code

2,651

Publication Type

Journal

Publication Title

Electronic Journal of Mathematical Analysis and Applications

Publication Link

https://ejmaa.journals.ekb.eg/

MainTitle

On the dynamics of a Riccati differential equation with perturbed delay

Details

Type

Article

Created At

18 Dec 2024