【摘要】 本文中,我们考虑一类带有扩散和时滞的捕食与被捕食系统。我们分析了系统的非负不变性,边界平衡点性质,全局渐近稳定性及永久持续生存性。在这一系统中,当时滞由0变到 r₀ 时,系统在平衡点附近发生 Hopf 分支。即当r增加通过临界值r₀时,从正平衡点分支出周期解。更多还原

【Abstract】 A system of retarded functional differential equations is proposed as a predator-prey model in two--patches. The invariance of non-negativity, nature of boundary equilibria,permanence and global stability are analyzed. We show that positive equilibrium is locallyasymptotically stable when time dalay Τ is suitable samll, while a loss of stability by a Hopfbifurcation can occur as the delay increases. That is, a family of periodic solutions bifurcatesfrom positive equilibrium as Τ passes through the critical value Τ₀.更多还原