Stability and bifurcation analysis of a discrete-time plant-herbivore model with harvesting effect

Mohammed Alsubhi; Rizwan Ahmed; Ibrahim Alraddadi; Faisal Alsharif; Muhammad Imran; Mohammed Alsubhi; Rizwan Ahmed; Ibrahim Alraddadi; Faisal Alsharif; Muhammad Imran

doi:10.3934/math.2024976

AIMS Mathematics

2024, Volume 9, Issue 8: 20014-20042. doi: 10.3934/math.2024976

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Research article

Stability and bifurcation analysis of a discrete-time plant-herbivore model with harvesting effect

1.
Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
2.
Department of Mathematics, Air University Multan Campus, Multan, Pakistan
3.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia

Received: 26 March 2024 Revised: 06 June 2024 Accepted: 12 June 2024 Published: 20 June 2024
MSC : 39A28, 39A30

The dynamics of plant-herbivore interactions are essential for understanding ecosystem stability and resilience. This article investigated the effects of incorporating a harvesting effect on the dynamics of a discrete-time plant-herbivore system. An analysis was performed to determine the existence and stability of fixed points. In addition, studies have shown that the system experienced transcritical, period-doubling, and Neimark-Sacker bifurcations. Moreover, we provided numerical simulations to substantiate our theoretical results. Our research indicated that harvesting in excessive amounts may have negative effects on the populations of both plants and herbivores. However, when harvesting was done at moderate levels, it promoted the coexistence and stability of both populations. The findings of our analysis provided a deep understanding of the intricate dynamics of ecological systems and underscored the need to use sustainable harvesting methods for the management and preservation of ecosystems.
- plant-herbivore system,
- harvesting effect,
- local stability analysis,
- local bifurcation analysis,
- computational analysis
Citation: Mohammed Alsubhi, Rizwan Ahmed, Ibrahim Alraddadi, Faisal Alsharif, Muhammad Imran. Stability and bifurcation analysis of a discrete-time plant-herbivore model with harvesting effect[J]. AIMS Mathematics, 2024, 9(8): 20014-20042. doi: 10.3934/math.2024976

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Abstract

The dynamics of plant-herbivore interactions are essential for understanding ecosystem stability and resilience. This article investigated the effects of incorporating a harvesting effect on the dynamics of a discrete-time plant-herbivore system. An analysis was performed to determine the existence and stability of fixed points. In addition, studies have shown that the system experienced transcritical, period-doubling, and Neimark-Sacker bifurcations. Moreover, we provided numerical simulations to substantiate our theoretical results. Our research indicated that harvesting in excessive amounts may have negative effects on the populations of both plants and herbivores. However, when harvesting was done at moderate levels, it promoted the coexistence and stability of both populations. The findings of our analysis provided a deep understanding of the intricate dynamics of ecological systems and underscored the need to use sustainable harvesting methods for the management and preservation of ecosystems.

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