计算机工程与应用
計算機工程與應用
계산궤공정여응용
COMPUTER ENGINEERING AND APPLICATIONS
2014年
17期
68-73,99
,共7页
恒化器%Ivlev型反应函数%不动点指数%单调方法
恆化器%Ivlev型反應函數%不動點指數%單調方法
항화기%Ivlev형반응함수%불동점지수%단조방법
chemostat%Ivlev response function%fixed point index%monotone method
刻画了一类带Ivlev型反应函数的非均匀恒化器竞争模型正解的存在域。利用不动点指数理论和上下解方法证明了在a 1λ?1且b 1σ?1的前提下，系统有正解的充要条件是a>r1(a'b)且b>r2(a'b)。结合单调方法和不动点指数理论，说明存在域Λ是R2+中的一个无界连通区域，其边界由两条递增的曲线Γ1：a=F1(b)和Γ2：b=F2(a)构成。证明了系统在存在域Λ的某个子区域内至少有两个正解。
刻畫瞭一類帶Ivlev型反應函數的非均勻恆化器競爭模型正解的存在域。利用不動點指數理論和上下解方法證明瞭在a 1λ?1且b 1σ?1的前提下，繫統有正解的充要條件是a>r1(a'b)且b>r2(a'b)。結閤單調方法和不動點指數理論，說明存在域Λ是R2+中的一箇無界連通區域，其邊界由兩條遞增的麯線Γ1：a=F1(b)和Γ2：b=F2(a)構成。證明瞭繫統在存在域Λ的某箇子區域內至少有兩箇正解。
각화료일류대Ivlev형반응함수적비균균항화기경쟁모형정해적존재역。이용불동점지수이론화상하해방법증명료재a 1λ?1차b 1σ?1적전제하，계통유정해적충요조건시a>r1(a'b)차b>r2(a'b)。결합단조방법화불동점지수이론，설명존재역Λ시R2+중적일개무계련통구역，기변계유량조체증적곡선Γ1：a=F1(b)화Γ2：b=F2(a)구성。증명료계통재존재역Λ적모개자구역내지소유량개정해。
The existence region of positive solutions in the unmixed chemostat with the Ivlev response function is por-trayed. It is shown that if a 1λ?1 and b 1σ?1 hold, then the necessary and sufficient conditions, where the system possesses positive solutions, are a>r1(a、b) and b>r2(a、b) by using the fixed point theory and the upper and lower solution method. Combining with the monotone method and the fixed point theory, it is proved that Λ is a connected unbounded region in R2+, whose boundary consists of two monotone nondecreasing curves Γ1:a=F1(b) and Γ2:b=F2(a) . It is shown that the system has at least two positive solutions in certain subregion of Λ.
