Investigating Global Stability and Bifurcation in an Ecological Dynamical System

Muhammad Salman Khan, Rizwan Niaz, Mohammed Ahmed Alomair, Mohamed Hussien and Ning Cai

Complexity, 2024, vol. 2024, 1-25

Abstract: We consider a continuous-time model describing the interaction between phytoplankton and zooplankton using a Holling type-II response. We then transform this continuous-time model into a discrete-time counterpart using a fractional-order discretization method. The paper explores the local stability of this obtained system concerning all equilibrium points and establishes the global asymptotic stability of its positive fixed point. The study also demonstrates that, under specific mathematical conditions, the system undergoes a Neimark–Sacker bifurcation around its positive equilibrium point. To effectively manage this bifurcation, two modified hybrid control techniques are introduced. The paper concludes by presenting illustrative numerical examples that validate the theoretical findings and assess the effectiveness and feasibility of the newly proposed control strategies. In addition, a comparative analysis is conducted between the modified hybrid techniques and an existing hybrid approach.

Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/complexity/2024/4970657.pdf (application/pdf)
http://downloads.hindawi.com/journals/complexity/2024/4970657.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:4970657

DOI: 10.1155/2024/4970657

Access Statistics for this article

More articles in Complexity from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().