Dynamics of a discrete-time prey-predator system with nonstandard finite difference scheme

Özlem Ak Gümüş; Özlem Ak Gümüş

doi:10.3934/math.2025802

AIMS Mathematics

2025, Volume 10, Issue 8: 17998-18023. doi: 10.3934/math.2025802

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Research article

Dynamics of a discrete-time prey-predator system with nonstandard finite difference scheme

Özlem Ak Gümüş ^,

Adıyaman University, Faculty of Arts and Sciences, Department of Mathematics, 02040, Adıyaman, Turkey

Received: 12 May 2025 Revised: 29 July 2025 Accepted: 01 August 2025 Published: 08 August 2025
MSC : 39A30, 92D25, 93C55, 34C23, 37N25

This study investigates the stability and bifurcation analysis of a discrete-time predator-prey system using a nonstandard finite difference scheme. We analytically demonstrate that the system undergoes a Neimark–Sacker bifurcation near its unique positive fixed point. To suppress the resulting chaotic dynamics, control strategies based on the OGY and state feedback control methods are implemented. Numerical simulations are conducted to support the theoretical analysis, confirming the effectiveness of the proposed control techniques.
- NSFD,
- prey-predator system,
- stability,
- bifurcation theory,
- chaos control
Citation: Özlem Ak Gümüş. Dynamics of a discrete-time prey-predator system with nonstandard finite difference scheme[J]. AIMS Mathematics, 2025, 10(8): 17998-18023. doi: 10.3934/math.2025802

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Abstract

This study investigates the stability and bifurcation analysis of a discrete-time predator-prey system using a nonstandard finite difference scheme. We analytically demonstrate that the system undergoes a Neimark–Sacker bifurcation near its unique positive fixed point. To suppress the resulting chaotic dynamics, control strategies based on the OGY and state feedback control methods are implemented. Numerical simulations are conducted to support the theoretical analysis, confirming the effectiveness of the proposed control techniques.

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