免费论文摘要：两类反馈分散模子的解的本质

??????? 物道学、化学和底栖生物学等天然学科中洪量的数学模子不妨归结为反馈分散方程,经过接洽反馈分散方程,不妨科学地证明和猜测天然局面,进而为题目的处置供给有理的道路,从而激动天然科学的兴盛;其余,反馈分散方程的接洽对数学也提出了很多挑拨性的题目,所以正惹起越来越多的数学家、物道学家、化学家、底栖生物学家和工程师的关心.?? ??????? 正文重要计划了两类反馈分散方程的解的本质,一类是具备功效反馈的捕食-食饵模子$$ left{?egin{array}{ll}???? displaystyle? u_{t} - dDelta u = -au + e frac{cv^{2}}{(1 + v)^{2}} u,???????????????? & xinOmega, t>0,???? displaystyle? v_{t} -? Delta v = r (1 - frac{v}{K}) v - frac{cv^{2}}{(1 + v)^{2}} u, & xinOmega, t>0,???? vspace{0.2cm}???? displaystyle? frac{partial u}{partial n} = frac{partial v}{partial n} = 0,??????? & xinpartialOmega, t>0,???? displaystyle? u(x,0) = u_{0}(x)geq 0, v(x,0) = v_{0}(x)geq 0 ,???????????????????? & xinOmega, ?end{array}?ight. $$一类是具备分散项的SIQS传抱病模子$$ left{?egin{array}{ll}??? displaystyle? u_{1t} - dDelta u_{1} = A - frac{eta u_{1}u_{2}}{u_{1}+u_{2}+u_{3}} - bu_{1} + gamma u_{2} + sigma u_{3},? & xinOmega, t>0,??? vspace{0.1cm}??? displaystyle? u_{2t} - dDelta u_{2} = frac{eta u_{1}u_{2}}{u_{1}+u_{2}+u_{3}} - (gamma + delta + b + alpha) u_{2} ,?????? & xinOmega, t>0,??? vspace{0.2cm}??? displaystyle? u_{3t} - dDelta u_{3} = delta u_{2} - (sigma + b + alpha) u_{3},???????????????????????????????????????????? & xinOmega, t>0,??? vspace{0.2cm}??? displaystyle? frac{partial u_{1}}{partial n} = frac{partial u_{2}}{partial n} = frac{partial u_{3}}{partial n}=0,??? & xinpartialOmega, t>0,?u_{i}(x,0) = u_{i,0}(x) > 0,?????????????????????????????????????????????????????????????????????????????????????? & i = 1,2,3,xinoverline{Omega}. ?end{array}?ight. $$????????? 在第一章中,正文运用扰动表面和分别表面的本领,计划了一类具备功效反馈的两物种间的捕食-食饵模子在Neumann边境前提下的分别局面.以分散系数为分别参数,证领会在确定前提下体例在平常数平稳解$ (u^{*},v^{*}) $ 邻近生存限制分别,并给出了分别点邻近解的构造,且限制分别不妨延拓成全部分别.??????? 在第二章中,正文计划了一类具备常数输出率和规范爆发率的SIQS模子,该类模子在SIS模子的普通上商量了对抱病者举行分隔的情景.计划了一类反馈分散体例在齐次Neumann边境前提下正解的渐近动作.应用线性化表面和左右解本领及其对应的缺乏迭代本领给出了常数解限制渐近宁静和全部渐近宁静的充溢前提.截止表白,当交战率很钟点,无病平稳点是全部渐近宁静的.

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