Bifurcation and chaos in a discrete activator-inhibitor system-Reference-Cited by-同舟云学术

Bifurcation and chaos in a discrete activator-inhibitor system

Published:2023 Issue:2 Volume:8 Page:4551-4574
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Khan Abdul Qadeer¹,Saleem Zarqa¹,Ibrahim Tarek Fawzi²³,Osman Khalid⁴,Alshehri Fatima Mushyih⁵,El-Moneam Mohamed Abd⁵

Affiliation:

1. Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan

2. Department of Mathematics, Faculty of Sciences and Arts (Mahayel), King Khalid University Abha, Saudi Arabia

3. Department of Mathematics, Faculty of Science, Mansoura University, Egypt

4. Department of Mathematics, Faculty of Sciences and Arts in Sarat Abeda, King Khalid University, Abha, Saudi Arabia

5. Department of Mathematics, Faculty of Science, Jazan University, Saudi Arabia

Abstract

<abstract><p>In this paper, we explore local dynamic characteristics, bifurcations and control in the discrete activator-inhibitor system. More specifically, it is proved that discrete-time activator-inhibitor system has an interior equilibrium solution. Then, by using linear stability theory, local dynamics with different topological classifications for the interior equilibrium solution are investigated. It is investigated that for the interior equilibrium solution, discrete activator-inhibitor system undergoes Neimark-Sacker and flip bifurcations. Further chaos control is studied by the feedback control method. Finally, numerical simulations are presented to validate the obtained theoretical results.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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