CAJ | 학술논문

在一类食饵捕食系统研究的基础上，增加食饵避难所这一影响因素，运用微分方程定性理论对系统平衡点的稳定性态、解的有界性进行了分析，通过对系统参数的讨论，得到了系统正平衡点存在且稳定的条件。根据张芷芬定理，构造Bendixson环域，找到了系统存在唯一稳定极限环的条件。研究表明，食饵避难所对系统具有稳定的影响，可以通过改变食饵避难所的多少来控制捕食者或被捕食者的种群密度，并给出了数值模拟结果。
재일류식이포식계통연구적기출상，증가식이피난소저일영향인소，운용미분방정정성이론대계통평형점적은정성태、해적유계성진행료분석，통과대계통삼수적토론，득도료계통정평형점존재차은정적조건。근거장지분정리，구조Bendixson배역，조도료계통존재유일은정겁한배적조건。연구표명，식이피난소대계통구유은정적영향，가이통과개변식이피난소적다소래공제포식자혹피포식자적충군밀도，병급출료수치모의결과。
The research of the stability of ecosystems has a profound meaning for a continuous, coordinate and stable development of ecological surroundings. This paper considers prey refuge, adding another parameter based on the research of prey-predator system. We apply the qualitative theory of differential equations to analyze the stability at the system equilibrium and the boundedness of solution. By discussion on systemic parameters, we obtain the condition of the existence and the stability of positive equilibrium in system. Bendixson cycle is constructed in a technique based on Zhang Zhifen theorem to find out the condition under which the system has a unique stable limit cycle. Our research shows that prey refuge has a stable influence on the system, and that the predator density or the prey density can be controlled by changing the amount of prey refuges. The numerical simulation result is also given