一类带有时滞的植物-传粉者-食草动物模型的动力学分析
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O 175.8

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国家自然科学基金资助项目(12071293)


Dynamic analysis of a plant-pollinator-herbivore model with time delay
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    摘要:

    针对传粉者与食草动物之间的关系,利用时滞微分方程理论,探讨了植物–传粉者–食草动物三者之间的动力学行为。确定了系统正平衡点的稳定性和产生Hopf分支的临界时滞,并根据中心流形定理和规范型理论得到了决定Hopf分支方向和周期解稳定性的条件,数值模拟验证了理论结果。研究结果表明:存在时滞的一个临界值,当时滞小于该临界值时,系统的正平衡点稳定;而当时滞大于该临界值时,系统会失稳,此时植物、传粉者和食草动物以周期振荡的形式共存。该研究从理论上揭示了时滞对植物、传粉者和食草动物三物种间相互作用的影响,即食草动物从摄食到完成自身转化所需的时间过长,会引起系统的周期振荡。

    Abstract:

    For the relationship between pollinators and herbivores, the theory of delay differential equations was used to explore the dynamical behavior of the plant-pollinator-herbivore triad. First, the stability of positive equilibrium of the system was analyzed and the critical value of time delay for the occurrence of Hopf bifurcation was obtained. Then, applying the center manifold theorem and normal form theory, the conditions for the direction of Hopf bifurcation and the stability of the bifurcation periodic solution were derived. Numerical simulations were performed to illustrate the theoretical results. The results show that if the time delay is less than a critical value, the system will stabilize at a positive equilibrium point. Conversely, if it is greater than this critical value, the system will destabilize, at which point the plants, pollinators, and herbivores coexist in periodic oscillations. The results theoretically reveal the effects of time delay on the tri-species interactions between plants, pollinators, and herbivores. That is, if the time taken for the herbivore from feeding to realizing its self-transformation is too long, it will induce the periodic oscillations of the system.

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徐婷玉,袁梦,未莹莹,原三领.一类带有时滞的植物-传粉者-食草动物模型的动力学分析[J].上海理工大学学报,2025,47(2):202-208.

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  • 收稿日期:2024-01-19
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  • 在线发布日期: 2025-05-21
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