一个浮游生物的数学模型的全局稳定性(英文)

Global stability of a mathematical model of plankton

考虑如下用来描述浮游动物-营养物相互作用时滞微分方程模型(dx(t))/dt=x(t)(α-bx(t) -c_sy(t)) +ry(t-T) ,dy(t)/dt=y(t)[(μx(t))/(k+x(t))-a-βy(t)] ,T≥0 ,其中,x(t)是营养物浓度,y(t)是浮游动物种群的度量,并且参数α,β,a,b,cs,k,r,μ为正常数.如果μ>a,α>cs(μβ-a)+μa-bka成立,则该系统的正平衡点是全局吸引的.也给出了正平衡点局部稳定的充分条件.

The differential delay model, which is introduced to simulate zooplankton-nutrient interaction, of the form dx（t） /dt=x（t）a-bx（t）-c,y（t））＋ry（t-T）,dy（t）/dt=y（t）（μx（t）/k＋x（t）-a-βy（t））,T≥0 is studied, where x （ t ） is the concentration of nutrient, y （ t ） is a measure of zooplankton population attime t and parameters α, β, a, b, c,, k, r,μ are positive constants. If ,μ 〉 a, and a 〉 cs（μ-a）/β＋abk/μ-a hold, then the positive steady state of this system is globally attractive. Some sufficient conditions on local stability of the steady state of the model are given.