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Mathematical Methods in the Applied Sciences
Article . 2026 . Peer-reviewed
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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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Nonstandard Finite Difference Theta Approaches to the Predator–Prey System

Authors: Nihal Özdoğan; Bahar Arslan;

Nonstandard Finite Difference Theta Approaches to the Predator–Prey System

Abstract

ABSTRACT In this paper, we propose nonstandard finite difference theta schemes for a well‐known Lotka‐Volterra model without the Allee effect and investigate the dynamical behavior of the discretized system. We prove that the scheme is dynamically consistent with the continuous model, preserving key properties such as the positivity of solutions and the stability of equilibrium points. Numerical experiments are conducted to validate the theoretical results and demonstrate the superiority of the proposed schemes over standard methods in maintaining these critical properties.

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Turkey
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Keywords

nonstandard finite difference theta method, positivity, predator-prey, stability, Lotka-Volterra system

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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