Dynamics of Three Species Food Chain Model with Holling type II Functional Response
Kaijen Cheng, Hongming You, Ting-Hui Yang
备注：
We found an error in Theorem 3.9, and a new version with different title "Global Stability of the Periodic Solution of the Three Level Food Chain Model with Extinction of Top Predator"
In this work, we revisit the classical Holling type II three species food chain model with a different viewpoint. Two critical parameters $λ_1$ and $λ_2$ dependent on other six parameters are defined. We show that local stabilities and existence of all equilibria can be reformulated by $λ_1$ and $λ_2$, and the complete classifications of parameters and its corresponding dynamics are given. Three global extinction results are showed by comparison principle analytically. Moreover, some interesting numerical simulations, including the chaotic phenomena, and the bi-stability phenomena, including equilibrium-cycle bi-stability and cycle-cycle bi-stability, are presented numerically. Finally, a brief discussion and biological implications are given.
Dynamics and Control of Additional Food Provided Prey-Predator Systems exhibiting Holling Type-III Functional Response and Intra-specific Competition among Predators
Global Dynamics and Time-Optimal Control Studies for Additional Food provided Holling Type-III Mutually Interfering Prey-Predator Systems with Applications to Pest Management
本文研究提供额外食物的 Holling III 型相互干扰猎物-捕食者系统，通过平衡点、全局稳定性分析及以食物质量和数量为参数的时间最优控制，证明合适额外食物可使系统达到猎物消除状态。
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
Dynamics of a predator-prey model with generalized Holling type functional response and mutual interference
相互干扰和猎物避难所是捕食者-猎物动力学的重要驱动因素。相互干扰的“指数”或程度在理论生态学中一直备受争议。本文研究了一类具有广义Holling型功能反应的捕食-食饵模型中相互干扰指数的相互作用。我们调查系统的稳定性，并推导出鞍结和Hopf分岔发生的条件。对于该模型，还得到了食饵种群灭绝的一个充分条件.此外，我们调查的猎物避难所对模型的种群动力学的影响，并推导出的猎物避难所，将产生持久性的人口的条件。我们通过数值模拟提供了额外的验证我们的分析结果。我们的研究结果与Gauss G. F（1934），这表明捕食者和猎物种群的灭绝是可能的在一个有限的时间段内-但引入避难所可以有效地导致持久性。
Deterministic and Stochastic Studies on Additional Food Provided Prey-Predator Systems with Group Defence among Prey and Mutual Interference among Predators
Gravity-Driven Eco-Epidemiological Dynamics in Tri-Trophic Food Chains
Indian Institute of Science Education and Research (IISER) Pune, India（印度科学教育研究所（普纳））；Institute for Physics and Astronomy, Technische Universität Berlin, Germany（柏林工业大学物理与天文研究所）；School of Technology and Architecture, SRH University of Applied Sciences HeidelbergLeipzig Campus, Germany（SRH应用科学大学海德堡-莱比锡校区技术与建筑学院）
