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author:

Fang, K. (Fang, K..) [1] | Wang, Y. (Wang, Y..) [2] | Chen, F. (Chen, F..) [3] | Chen, X. (Chen, X..) [4]

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Scopus

Abstract:

This study investigates a modified Lotka–Volterra commensalism system that incorporates the weak Allee effect in prey and symmetric (equal harvesting effort for both species) non-selective harvesting, addressing a critical gap in ecological modeling. Unlike previous work, we rigorously examine how the interaction between the Allee effect and harvesting disrupts system stability, giving rise to novel bifurcation phenomena and population collapse thresholds. Using eigenvalue analysis and the Dulac–Bendixson criterion, we derive sufficient conditions for the existence and stability of equilibria. We find that harvesting destabilizes the system by inducing two saddle-node bifurcations. Notably, prey abundance can increase with greater Allee intensity under controlled harvesting—a rare and counterintuitive ecological outcome. Moreover, exceeding a critical harvesting threshold drives both species to extinction, while controlled harvesting allows sustainable coexistence. Numerical simulations support these analytical findings and identify critical parameter ranges for species coexistence. These results contribute to theoretical ecology and offer insights for designing sustainable harvesting strategies that balance exploitation with conservation. © 2025 by the authors.

Keyword:

Allee effect bifurcation harvest Lotka–Volterra commensal symbiosis model

Community:

  • [ 1 ] [Fang K.]Department of Mathematics and Statistics, Fuzhou University Zhicheng College, Fuzhou, 350002, China
  • [ 2 ] [Wang Y.]Department of Mathematics Research, Fujian Institute of Education, Fuzhou, 350001, China
  • [ 3 ] [Chen F.]School of Mathematics and Statistics, Fuzhou University, Fuzhou, 350108, China
  • [ 4 ] [Chen X.]Department of Mathematics Research, Fujian Institute of Education, Fuzhou, 350001, China

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Source :

Symmetry

ISSN: 2073-8994

Year: 2025

Issue: 6

Volume: 17

2 . 1 4 3

JCR@2018

Cited Count:

WoS CC Cited Count:

SCOPUS Cited Count:

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 4

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