噪声对捕食者—被捕食者模型中猎物灭绝时间的影响  

Effects of noises on the mean extinction time of prey for a preador-prey model

作　　者：王国威[1,2] 付燕[3] 

机构地区：[1]南昌工学院基础教学部,南昌330108 [2]南昌工学院非线性力学重点实验室,南昌330108 [3]南昌工学院民族教育学院,南昌330108

出　　处：《华中师范大学学报（自然科学版）》2016年第3期363-368,共6页Journal of Central China Normal University：Natural Sciences

基　　金：江西省教育厅科学技术研究项目(GJJ151240);南昌工学院科技计划项目(GJKJ-15-34);南昌工学院非线性力学重点实验室资助项目

摘　　要：把平均灭绝时间引入到捕食者—被捕食者模型,利用最快下降法,得到了该模型的平均首次通过时间的表达式,分析了噪声强度及其关联对被捕食者(猎物)的平均灭绝时间的影响.对计算结果的数值分析结果表明:(1)当猎物处于x-这个稳定态时,加性噪声强度D增加弱化猎物群体的稳定性,D的增加导致猎物灭绝时间T+(x-→xu)减小.同时,乘性噪声强度Q增加强化猎物群体的稳定性,Q的增加导致猎物灭绝时间T+(x-→xu)增大.(2)当猎物处于x+这个稳定态时,加性噪声强度D增加强化猎物群体的稳定性,乘性噪声强度Q增加弱化猎物群体的稳定性,Q的增加导致猎物灭绝时间T-(x+→xu)减小.(3)T+(x-→xu)随λ变化以D为参量的曲线出现了一个类似于共振峰的极大值,λ存在一个范围(0.4<λ<0.8),在这个范围内,猎物的平均灭绝时间较长,猎物不易灭绝,这对防止猎物灭绝具有积极意义.(4)T-(x+→xu)随D变化以Q为参量的曲线出现了一个类似于共振峰的极大值,此时一定范围内的乘性噪声强度Q(Q>0.5)会造成极大值消失的情况,这会导致猎物群体系统的稳定性下降,平均灭绝时间变短,对防止猎物灭绝是不利的.The mean extinction time is introduced to a predator-prey model based on the theoretical results of Suman Kumar Banik.By virtue of the steepest descent method,the analytical expressions of the mean first-passage time（MFPT）of the system is obtained,the effects of noises on the mean extinction time of prey is investigated.The result shows that：（1）When the prey is at x-,the additive noise intensity weaken the stability of the prey system,and increasing D leads to smaller T＋（x-→xu）.At the same time,multiplicative noise intensity strength the stability of the prey system,and increasing Qleads to longer T＋（x- →xu）.（2）When the prey is at x＋,the additive noise intensity strength the stability of the prey system,but the multiplicative noise intensity weaken the stability of the prey system,and increasing Qleads to smaller T-（x＋→xu）.（3）The curve of T＋（x-→xu）vsλpresents a peak which is similar to the stochastic resonance peak,andλexsits the range（0.4λ0.8）when the intensity of noise are some certain values,the mean extinction time of prey are longer than others,it makes positive significance to prevent prey from extinction.（4）The curve of T-（x＋ →xu）appears a similar paek with the increasing of D,at the same time,the peak disppeared at some certain values of Q（Q0.5）,that is to say,the stability of the system is weakened,and prey are more prone to extinction.

关 键 词：捕食者—被捕食者模型 噪声 平均灭绝时间 环境波动 稳定性 

分 类 号：O411.1[理学—理论物理]