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Dynamics of a Modified Lotka–Volterra Commensalism System Incorporating Allee Effect and Symmetric Non-Selective Harvest

by Kan Fang, Yiqin Wang, Fengde Chen and Xiaoying Chen

Symmetry 2025, 17(6), 852; https://doi.org/10.3390/sym17060852 - 30 May 2025

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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. Full article

(This article belongs to the Special Issue Mathematics: Feature Papers 2025)

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25 pages, 13842 KiB

Open AccessArticle

Research into the Peculiarities of the Individual Traction Drive Nonlinear System Oscillatory Processes

by Alexander V. Klimov, Baurzhan K. Ospanbekov, Andrey V. Keller, Sergey S. Shadrin, Daria A. Makarova and Yury M. Furletov

World Electr. Veh. J. 2023, 14(11), 316; https://doi.org/10.3390/wevj14110316 - 20 Nov 2023

Cited by 6 | Viewed by 1906

Abstract

Auto-oscillations may occur in moving vehicles in the area where the tire interacts with the support base. The parameters of such oscillations depend on the sliding velocity in the contact patch. As they negatively affect the processes occurring in the electric drive and the mechanical transmission, reducing their energy efficiency, such processes can cause failures in various elements. This paper aims to conduct a theoretical study into the peculiarities of oscillatory processes in the nonlinear system and an experimental study of the auto-oscillation modes of an individual traction drive. It presents the theoretical basis used to analyze the peculiarities of oscillation processes, including their onset and course, the results of simulation mathematical modeling and the experimental studies into the oscillation phenomena in the movement of the vehicle towards the supporting base. The practical value of this study lies in the possibility to use the results in the development of algorithms for the exclusion of auto-oscillation phenomena in the development of vehicle control systems, as well as to use the auto-oscillation processes onset and course analysis methodology to design the electric drive of the driving wheels. Full article

(This article belongs to the Topic Advanced Electric Vehicle Technology)

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10 pages, 5943 KiB

Open AccessArticle

Dynamic Behavior Investigation of a Novel Epidemic Model Based on COVID-19 Risk Area Categorization

by Jiaji Pan, Siqiang Sun, Yixuan He, Shen Ren, Qing Li, Zhongxiang Chen and Hao Feng

Fractal Fract. 2022, 6(8), 410; https://doi.org/10.3390/fractalfract6080410 - 26 Jul 2022

Cited by 2 | Viewed by 1834

Abstract

This study establishes a compartment model for the categorized COVID-19 risk area. In this model, the compartments represent administrative regions at different transmission risk levels instead of individuals in traditional epidemic models. The county-level regions are partitioned into High-risk (H), Medium-risk (M), and Low-risk (L) areas dynamically according to the current number of confirmed cases. These risk areas are communicable by the movement of individuals. An LMH model is established with ordinary differential equations (ODEs). The basic reproduction number

R_{0}

is derived for the transmission of risk areas to determine whether the pandemic is controlled. The stability of this LHM model is investigated by a Lyapunov function and Poincare–Bendixson theorem. We prove that the disease-free equilibrium (

R_{0}

< 1) is globally asymptotically stable and the disease will die out. The endemic equilibrium (

R_{0}

> 1) is locally and globally asymptotically stable, and the disease will become endemic. The numerical simulation and data analysis support the previous theoretical proofs. For the first time, the compartment model is applied to investigate the dynamics of the transmission of the COVID-19 risk area. This work should be of great value in the development of precision region-specific containment strategies. Full article

(This article belongs to the Special Issue Numerical and Analytical Methods for Differential Equations and Systems)

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