Global dynamics of an amensalism system with Michaelis-Menten type harvesting
Global dynamics of an amensalism system with Michaelis-Menten type harvesting
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DOI：
10.3934/era.2023027
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发表时间：
2022
影响因子：
0.8
通讯作者：
Ming Zhao;Yudan Ma;Yunfei Du
中科院分区：
文献类型：
--
作者：
Ming Zhao;Yudan Ma;Yunfei Du
本文研究了一类新的第二种群具有非线性Michaelis-Menten型收获的偏害系统。首先，我们阐明了系统所有可能的平衡点的拓扑类型。然后，通过分支分析讨论了系统在无穷远点附近的行为、闭轨道的存在性以及鞍形连接，并给出了系统的全局相图.最后，为了便于比较，我们进一步给出了一个新的无收获模型的完全全局动力学。数值模拟表明，具有收获的系统具有更丰富的动力学，例如保持第一个物种的灭绝或更慢地接近稳态。我们的研究将为我们更好地理解具有收获效应的偏害系统的动态复杂性提供有用的信息。
In this work, a new amensalism system with the nonlinear Michaelis-Menten type harvesting for the second species is studied. Firstly, we clarify topological types for all possible equilibria of the system. Then, the behaviors near infinity and the existence of closed orbits as well as saddle connections of the system are discussed via bifurcation analysis, and the global phase portraits of the model are also illustrated. Finally, for the sake of comparison, we further offer a new complete global dynamics of the model without harvesting. Numerical simulations show that the system with harvesting has far richer dynamics, like preserving the extinction of the first species or approaching the steady-state more slowly. Our research will provide useful information which may help us have a better understanding to the dynamic complexity of amensalism systems with harvesting effects.