Abstract：
This paper investigates the dynamics of a tritrophic food chain model incorporating an Allee effect, sexually reproductive generalist top predators, and Holling type IV and Beddington-DeAngelis functional responses for interactions across different trophic levels. Analytically, we explore the feasible equilibria, their local stability, and various bifurcations, including Hopf, saddle-node, transcritical, and Bogdanov-Takens bifurcations. Numerical findings suggest that higher Allee intensity in prey growth leads to the inability of species coexistence, resulting in a decline in species density. Likewise, a lower reproduction rate and a higher strength of intraspecific competition among top predators also prevent the coexistence of species. Conversely, a rapid increase in the reproduction rate and a decrease in the strength of intraspecific competition among top predators enhance the densities of prey and top predators while decreasing intermediate predator density. We also reveal the presence of bistability and tristability phenomena within the system. Furthermore, we extend our autonomous model to its nonautonomous counterpart by introducing seasonally perturbed parameters. Numerical analysis of the nonautonomous model reveals that higher seasonal strength in the reproduction rate and intraspecific competition of top predators induce chaotic behavior, which is also confirmed by the maximum Lyapunov exponent. Additionally, we observe that seasonality may lead to the extinction of species from the ecosystem. Factors such as the Allee effect and growth rate of prey can cause periodicity in population densities. Understanding these trends is critical for controlling changes in population density within the ecosystem. Ecologists, environmentalists, and policymakers stand to benefit significantly from the invaluable insights garnered from this study. Specifically, our findings offer pivotal guidance for shaping future strategies aimed at safeguarding biodiversity and maintaining ecological stability amidst changing environmental conditions. By contributing to the existing body of knowledge, our study advances the field of ecological science, enhancing the comprehension of predator-prey dynamics across diverse ecological conditions.
摘要：
本文研究了包含Allee效应的三养食物链模型的动力学，性生殖通才顶级掠食者，以及HollingIV型和Beddington-DeAngelis对不同营养级相互作用的功能响应。分析,我们探索可行的均衡，当地的稳定,和各种分叉，包括Hopf,鞍形节点,超临界,和Bogdanov-Takens分叉.数值结果表明，猎物生长中更高的Allee强度导致物种无法共存，导致物种密度下降。同样，顶级捕食者之间较低的繁殖率和较高的种内竞争强度也阻止了物种的共存。相反，繁殖率的迅速提高和顶级捕食者之间种内竞争强度的降低会增加猎物和顶级捕食者的密度，同时降低中等捕食者的密度。我们还揭示了系统中双稳态和三稳态现象的存在。此外，我们通过引入季节性扰动参数将我们的自治模型扩展到其非自治对应物。非自治模型的数值分析表明，繁殖率和顶级捕食者种内竞争的较高季节强度会引起混沌行为，最大Lyapunov指数也证实了这一点。此外,我们观察到季节性可能导致物种从生态系统中灭绝。诸如Allee效应和猎物的生长速率之类的因素会导致种群密度的周期性。了解这些趋势对于控制生态系统内人口密度的变化至关重要。生态学家,环保主义者,政策制定者将从这项研究中获得的宝贵见解中受益匪浅。具体来说,我们的研究结果为制定旨在在不断变化的环境条件下保护生物多样性和维持生态稳定的未来战略提供了关键指导。通过对现有知识体系的贡献，我们的研究推进了生态科学领域，增强对不同生态条件下捕食者-猎物动态的理解。
