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)(a-bx(t)-csy(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,c,k,r,μ为正常数.如果μ＞ a, α＞cx(μ-a)/β+abk/μ-a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)-csy(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 at time t and parameters α, β, a, b, c,, k, r, μ are positive constants. If μ＞ a, and α＞cx(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.
展开▼
