应用数学
應用數學
응용수학
MATHEMATICA APPLICATA
2012年
1期
131-139
,共9页
捕食模型%阶段结构%时滞%稳定性%Hopf分支
捕食模型%階段結構%時滯%穩定性%Hopf分支
포식모형%계단결구%시체%은정성%Hopf분지
Predator-prey model%Stage structure%Time delay%Stability%Hopf bifur cation
研究一类具有阶段结构和时滞的捕食模型.通过特征方程分别分析了正平衡点和边界平衡点的局部稳定性,到了系统Hopf分支存在的充分条件.通过规范型理论和中心流型定理,给出了确定Hopf分支方向和分支周期解的稳定性的计算公式.
研究一類具有階段結構和時滯的捕食模型.通過特徵方程分彆分析瞭正平衡點和邊界平衡點的跼部穩定性,到瞭繫統Hopf分支存在的充分條件.通過規範型理論和中心流型定理,給齣瞭確定Hopf分支方嚮和分支週期解的穩定性的計算公式.
연구일류구유계단결구화시체적포식모형.통과특정방정분별분석료정평형점화변계평형점적국부은정성,도료계통Hopf분지존재적충분조건.통과규범형이론화중심류형정리,급출료학정Hopf분지방향화분지주기해적은정성적계산공식.
A predator-prey system with time delay due to the gestation of the predator and stage structure for both the predator and the prey is proposed and investigated.By analyzing the corresponding characteristic equations,the stability of a positive equilibrium and two boundary equilibria of the system is discussed,respectively.Further,the existence of Hopf bifurcations at the positive equilibrium is also studied.By using the normal form theory and center manifold theorem,formulae determining the direction of bifurcations and the stability of bifurcating periodic solutions are given.
