毒素影响下具反馈控制和非线性抑制项影响的一类三种群捕食−竞争离散时滞系统的持久性分析  

Persistence analysis of a three-species predation-competition discrete time-delay model with feedback control and nonlinear inhibition in the effects of toxicants

作　　者：蔡旖旎 刘萍[1] 李艳 CAI Yi-ni;LIU Ping;LI Yan(School of Mathematics and Statistics,Yunnan University,Kunming 650500,Yunnan,China)

机构地区：[1]云南大学数学与统计学院,云南昆明650500

出　　处：《云南大学学报（自然科学版）》2022年第3期435-443,共9页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(11961078,11561072).

摘　　要：持久性是生态系统的重要性质.由于外界因素对生态系统的干扰是不可避免的,提出了一类新的具有时滞和反馈控制、且受到毒素和非线性抑制项影响的三种群捕食−竞争离散系统,通过差分方程比较原理和相关不等式计算技巧,得到了系统持久性生存的充分条件,推广了前人的相关研究结果.结果显示,时滞、反馈控制和毒素均会影响系统的持久性.进一步,实例验证了理论结果的可行性.Persistence is an important property of the ecosystem.Since the interference of external factors on the ecosystem is inevitable,a new three-species predation-competition discrete model with time delay and feedback control with the effects of toxicants and nonlinear inhibition terms was proposed.By using the comparison principle of difference equations and calculation techniques related to inequalities,sufficient conditions for the permanence of the system was obtained.The results of previous studies have been promoted.The results show that time delays,feedback control and toxic substances will all affect the persistence of the system.Furthermore,an example was given to verify the feasibility of the theoretical result.

关 键 词：捕食−竞争离散系统 持久性 反馈控制 Holling-Ⅲ功能反应 

分 类 号：O175.14[理学—数学]