Rich dynamics of a discrete two dimensional predator–prey model using the NSFD scheme

In this paper, we consider a two-species predator–prey model with Holling type III functional response and non-linear predator harvesting. The proposed model is discretized using a non-standard finite difference scheme (NSFD). The stability of different equilibrium points are analyzed. Also, the con...

Full description

Saved in:
Bibliographic Details
Published inMathematics and computers in simulation Vol. 225; pp. 992 - 1018
Main Authors Mokni, Karima, Ch-Chaoui, Mohamed, Mondal, Bapin, Ghosh, Uttam
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.11.2024
Subjects
Chaos control
Discrete predator–prey model
Harvesting
Non-standard finite difference
Pole placement method
Non-standard finite difference
Discrete predator–prey model
Pole placement method
Chaos control
Harvesting
Online AccessGet full text
ISSN0378-4754
DOI10.1016/j.matcom.2023.09.024

Cover

More Information
Summary:In this paper, we consider a two-species predator–prey model with Holling type III functional response and non-linear predator harvesting. The proposed model is discretized using a non-standard finite difference scheme (NSFD). The stability of different equilibrium points are analyzed. Also, the conditions of various types of bifurcations likely: Transcritical, Neimark–Sacker bifurcation (NSB), and Flip (Period doubling) bifurcation (PDB) have been established along with chaos control strategies. The numerical results indicate that the system exhibits different patterns of solutions, including single, two, and higher periodicity. Using Lyapunov exponents and bifurcation diagrams, chaotic solutions are verified. Two model parameters were drawn simultaneously in the attractor basin, which yielded different periodic solutions compared to the continuous dynamical system. Lastly, the pole placement method (PPM) has been used to control chaos in the proposed discrete ecological model.
ISSN:0378-4754
DOI:10.1016/j.matcom.2023.09.024