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具有避难所和饱和效应离散偏害系统的持久性

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提出具有避难所和饱和效应的离散偏害系统,得到一组保证系统持久的充分性条件.研究结果表明,避难所和第二个种群的密度对系统的持久起到重要作用;在系统持久的条件下,系统可能有唯一全局稳定的正平衡点,也可能有周期正解存在;存在阈值k0,当k>k0 时,系统是持久的.数值模拟表明,若k0<0时,避难所不会影响系统的持久性,但是随着避难所增大,第一个种群的持久域上下界都逐步增大;若k0>0时,随着k趋于k0,第一个种群持久的下界也趋于0,这意味着当k趋于k0 时,种群的数量很小,也就意味着种群抗干扰能力减弱,容易发生灭绝的风险;在k>k0 时,虽然系统会持久,但是第一个种群的动力学行为还是比较复杂,有多种可能性.离散系统的动力学行为远比对应的连续系统的动力学行为复杂.
Permanence of a discrete amensalism system with refuge and saturation effect
A discrete amensalism system with refuge and saturation effects is proposed,and a set of sufficient conditions to ensure the permanence of the system are obtained.Research results showed that the refuge and the second population played an important role in the permanence of the system.Under the condition of system permanence,there may be a unique globally stable positive equilibrium and there may also be periodic positive solutions;There is a threshold k0.If k0<0,the system is permanence and the numerical simulation shows that the refuge will not affect the permanence of the system,but with the increase of the refuge,the upper and lower bounds of the permanence domain of the first population gradually increase.If k0>0and k as tends to k0,the lower bound of the permanence of the first population also tends to 0,which means that when k tends to k0,the population number is small,which means that the anti-interference ability of the population is weakened and the risk of extinction is easy to occur;Although the system is permanence,the dynamics of the first population is complex and has many possibilities,when k>k0.The dynamic behavior of the discrete system is much more complex than that of the corresponding continuous system.

discrete partial damage systemsaturation effectshelterpersistencedynamic behavior

种艳波、薛亚龙、陈尚铭

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福州大学 数学与统计学院,福建 福州 350108

宁德师范学院 数理学院,福建 宁德 352100

离散偏害系统 饱和效应 避难所 持久性 动力学行为

福建省自然科学基金资助项目福建省自然科学基金资助项目

2020J014992021J011155

2024

宁德师范学院学报(自然科学版)
宁德师范学院

宁德师范学院学报(自然科学版)

影响因子:0.303
ISSN:2095-2481
年,卷(期):2024.36(1)
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