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首页> 外文期刊>Mathematical Biosciences: An International Journal >Study of a tri-trophic prey-dependent food chain model of interacting populations
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Study of a tri-trophic prey-dependent food chain model of interacting populations

机译：相互作用种群的三养性依赖猎物的食物链模型研究

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The current paper accounts for the influence of intra-specific competition among predators in a prey dependent tri-trophic food chain model of interacting populations. We offer a detailed mathematical analysis of the proposed food chain model to illustrate some of the significant results that has arisen from the interplay of deterministic ecological phenomena and processes. Biologically feasible equilibria of the system are observed and the behaviours of the system around each of them are described. In particular, persistence, stability (local and global) and bifurcation (saddle-node, transcritical, Hopf-Andronov) analysis of this model are obtained. Relevant results from previous well known food chain models are compared with the current findings. Global stability analysis is also carried out by constructing appropriate Lyapunov functions. Numerical simulations show that the present system is capable enough to produce chaotic dynamics when the rate of self-interaction is very low. On the other hand such chaotic behaviour disappears for a certain value of the rate of self interaction. In addition, numerical simulations with experimented parameters values confirm the analytical results and shows that intra-specific competitions bears a potential role in controlling the chaotic dynamics of the system; and thus the role of self interactions in food chain model is illustrated first time. Finally, a discussion of the ecological applications of the analytical and numerical findings concludes the paper.
机译：当前的文件解释了在相互依赖的种群的依赖猎物的三营养食物链模型中，捕食者之间种内竞争的影响。我们对提出的食物链模型进行了详细的数学分析，以说明确定性生态现象和过程之间相互作用所产生的一些重要结果。观察到系统的生物可行平衡，并描述了每个系统周围系统的行为。特别是，获得了该模型的持久性，稳定性（局部和全局）和分叉（鞍节点，跨临界，Hopf-Andronov）分析。将先前众所周知的食物链模型的相关结果与当前发现进行比较。通过构造适当的Lyapunov函数，还可以进行全局稳定性分析。数值模拟表明，当自交互率非常低时，本系统足以产生混沌动力学。另一方面，这种混沌行为在一定程度的自我互动中消失了。此外，用实验参数值进行的数值模拟证实了分析结果，并表明种内竞争在控制系统混沌动力学中起着潜在的作用。因此，首次说明了自我互动在食物链模型中的作用。最后，对分析和数值结果在生态学上的应用进行了总结。

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