具有成熟延迟的化学计量生产者-食草动物模型的动力学

IF 0.4 Q4 MATHEMATICS, APPLIED Mathematics in applied sciences and engineering Pub Date : 2022-02-06 DOI:10.5206/mase/14332
Hua Zhang, Hao Wang, Ben Niu
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引用次数: 0

摘要

生态化学计量提供了一种通过微观透镜研究宏观现象的多尺度方法。本文提出并研究了一个具有成熟延迟的化学计量生产者-食草动物模型。化学计量和延迟之间的相互作用是新颖的,并在经典延迟驱动的周期解之外带来了更有趣的见解。例如,当生产者中的最小磷碳比降低时,可能会出现周期加倍的混沌途径。在数学上,我们建立了正平衡存在和稳定的条件,并研究了正平衡下Hopf分岔的发生。分析结果表明,时滞可以通过跨临界分岔、鞍节点分岔和Hopf分岔改变正平衡的个数和稳定性,并进一步决定了掠器的灭绝。我们的小延迟模型在光强方面与LKE模型类似,在适当的光强下存在Rosenzweig富集悖论。我们绘制了分叉图,显示了由延迟、光强、磷有效性和转化效率驱动的丰富动力学,包括大的延迟可以在中等光强下驱动食草动物灭绝,这有利于食草动物在没有延迟的情况下生存;极限循环可能出现,然后随着延迟的增加而消失;给定相同的初始条件,具有不同延迟值的解可以趋向于不同的吸引子。
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Dynamics of a stoichiometric producer-grazer model with maturation delay
Ecological stoichiometry provides a multi-scale approach to study macroscopic phenomena via microscopic lens. A stoichiometric producer-grazer model with maturation delay is proposed and studied in this paper. The interaction between stoichiometry and delay is novel and leads to more interesting insights beyond classical delay-driven periodic solutions. For example, the period doubling route to chaos can occur as the minimal phosphorous:carbon ratio in producer decreases. Mathematically, we establish the conditions for the existence and stability of positive equilibria, and study the occurrence of Hopf bifurcation at positive equilibria. Analytic results show that delay can change the number and stability of positive equilibria through transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation, and it further determines the grazer's extinction. Our model with a small delay behaves like LKE model in terms of light intensity, and Rosenzweig's paradox of enrichment exists in a suitable light intensity. We plot bifurcation diagrams and show rich dynamics driven by delay, light intensity, phosphorous availability, and conversion efficiency, including that a large delay can drive the grazer to go extinct in an intermediate light intensity that is favorable for the survival of the grazer when there is no delay; a limit cycle can appear, then disappear as the delay increases; given the same initial condition, solutions with different delay values can tend to different attractors.
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CiteScore
1.40
自引率
0.00%
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0
审稿时长
21 weeks
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