CAJ | 학술논문

证明了一类具扩散的捕食与被捕食Lotka-Volterra模型的如下性质：当该模型存在正平衡点时，它的一切正解是有界的，并且是强持续生存的；当扩散率较小时，系统的正平衡点是稳定的；当扩散率增大且在某一开区间变化时，系统的正平衡点是不稳定的，而且分支出唯一的小振幅空间周期解；当扩散率继续增大时，系统的正平衡点又变成稳定的．
증명료일류구확산적포식여 피포식Lotka-Volterra모형적여하성질：당해모형존재정평형점시，타적일절정해시유계 적，병차시강지속생존적；당확산솔교소시，계통적정평형점시은정적；당확산솔증대차재 모일개구간변화시，계통적정평형점시불은정적，이차분지출유일적소진폭공간주기해；당 확산솔계속증대시，계통적정평형점우변성은정적．
A class of Lotka-Volterra model of diffuse predat or-prey is analysed,which has the following features:if there is a positive bal ance point in this system,all its positive balance points are bounded and st rongly persistence;if the model has a small diffuse rate,its positive balance po int will fluctuate steadily,but when the diffuse rate increases to a certain deg ree and keeps changing in a certain open interval,the positive balance point will fluctuate unsteadily and branch out one periodic solution within a sm all amplitude;if the diffuse rate keeps increasing and goes beyond the certain d egree,the positive balance point will fluctuate in a steady rate again.