一類帶有時(shí)滯的植物-傳粉者-食草動(dòng)物模型的動(dòng)力學(xué)分析

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中圖分類號(hào)：0175.8 文獻(xiàn)標(biāo)志碼：A

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

XU Tingyu， YUAN Meng， WEI Yingying， YUAN Sanling （College of Science， University of Shanghai for Science and Technology，Shanghai 2Ooo93， China）

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 willdestabilize， 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， pollnators， and herbivores. That is， if the time taken for the herbivore from feeding to realizing its selftransformation is too long， it will induce the periodic oscillations of the system.

Keywords： plant-pollinator-herbivore model; pollination mutualism; time delay; Hopf bifurcation

傳粉者和食草動(dòng)物是植物進(jìn)化的主要驅(qū)動(dòng)力。（剩余6590字）