Stability analysis of a modified Leslie-Gower predation model with weak Allee effect on the prey

聚合是一把双刃剑：恐惧、Allee效应与有限时间崩溃

Aggregation as a Double-Edged Sword: Fear, Allee Effects, and Finite-Time Collapse

研究通过疾病-捕食模型揭示，猎物聚合在恐惧和Allee效应下会加速生态系统有限时间崩溃，并首次量化了行为与人口参数对崩溃速度的影响。

具有加性 Allee 效应的捕食者–食饵系统中极限环与分岔的 Isola 与蘑菇动力学

Isola and mushroom dynamics of limit cycles and bifurcations in a predator-prey system with additive Allee effect

该研究结合解析与数值方法分析含加性 Allee 效应及广义 Holling IV 响应的捕食系统，揭示多种高阶分岔及极限环 isola、蘑菇结构，并阐明 Allee 强度对灭绝与共存的影响。

一类具有 Allee 效应的捕食者-猎物模型的研究

A study on a class of predator-prey models with Allee effect

本文研究了受常数捕获且具 Allee 效应的 Holling type I Leslie-Gower 捕食者-猎物模型的动力学行为，分析了多种平衡点及鞍结分岔和 Hopf 分岔条件，并证明了系统在尖点附近发生余维 2 Bogdanov-Takens 分岔。

Modelling and analysis of a modified May-Holling-Tanner predator-prey model with Allee effect in the prey and an alternative food source for the predator

In the present study, we have modified the traditional May-Holling-Tanner predator-prey model used to represent the interaction between least weasel and field-vole population by adding an Allee effect (strong and weak) on the field-vole population and alternative food source for the weasel population. It is shown that the dynamic is different from the original May-Holling-Tanner predator-prey interaction since new equilibrium points have appeared in the first quadrant. Moreover, the modified model allows the extinction of both species when the Allee effect (strong and weak) on the prey is incl…

修正 Leslie-Gower 模型中的奇异分岔

Singular bifurcations in a modified Leslie-Gower model

研究具弱Allee效应的Leslie-Gower捕食系统，通过引入小时间尺度参数构建慢-快系统，利用吹胀法严格分析了由退化超越临界分岔组织的退化情形，并确定了奇异Hopf分岔的临界性，数值与解析证实了Takens-Bogdanov点的存在。

A Holling-Tanner predator-prey model with strong Allee effect

We analyse a modified Holling-Tanner predator-prey model where the predation functional response is of Holling type II and we incorporate a strong Allee effect associated with the prey species production. The analysis complements results of previous articles by Saez and Gonzalez-Olivares (SIAM J. Appl. Math. 59 1867-1878, 1999) and Arancibia-Ibarra and Gonzalez-Olivares (Proc. CMMSE 2015 130-141, 2015)discussing Holling-Tanner models which incorporate a weak Allee effect. The extended model exhibits rich dynamics and we prove the existence of separatrices in the phase plane separating basins o…

A modified May-Holling-Tanner predator-prey model with multiple Allee effects on the prey and an alternative food source for the predator

We study a predator-prey model with Holling type I functional response, an alternative food source for the predator, and multiple Allee effects on the prey. We show that the model has at most two equilibrium points in the first quadrant, one is always a saddle point while the other can be a repeller or an attractor. Moreover, there is always a stable equilibrium point that corresponds to the persistence of the predator population and the extinction of the prey population. Additionally, we show that when the parameters are varied the model displays a wide range of different bifurcations, such a…

Hierarchical Model with Allee Effect, Immigration, and Holling Type II Functional Response

In this paper, we discuss a hierarchical model, based on a Ricker competition model. The species considered are competing for resources and may be subject to an Allee effect due to mate limitation, anti-predator vigilance or aggression, cooperative predation or resource defense, or social thermoregulation. The species may be classified into a more dominant species and less dominant or ``wimpy" species or just as a predator and prey. The model under consideration also has components taking into account immigration in both species and a more structured Holling type II functional response. Local …

揭示具有捕食者Allee效应的奇异摄动捕食者-猎物系统中canard环的动力学与全局行为

Unveiling the dynamics of canard cycles and global behaviour in a singularly perturbed predator-prey system with Allee effect in predator

本研究通过数学分析揭示具有捕食者Allee效应的慢快Leslie-Gower模型的丰富动力学，包括canard环、分岔及全局稳定性，并验证了不同初始条件下的共存或灭绝模式。