| TYPE K MONOTONE SYSTEMS WITH AN ORDER-INCREASING INVARIANT FUNCTION |
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| 作者姓名： | Jiang Jifa |
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| 作者单位： | Department of Mathematics，The University of Science and Technology of China，Hefei 230036，China. |
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| 摘 要： | 51.IntroductionBeginingwiththepath-breakingworkofM.W.HirschI1-4]forcooperativesystemsandmonotonesemiflows,thereisnowanextensiveliteratureoncooperativesystemsandmoncatonedynamicalsystems.Assumingthatthesystemiscooperativeandirreducible,HirschshowedthataImosteveryforwardorbitwithcompactclosure,inthesenseofLebesguemeasure,tendstoequilibriaast- oc(see2,Theorem4.l]).Asimilarresultholdsforastronglymonotonesemifiowonastronglyorderspace(see4,Theoremo.1]).Manypeoplehavegivensomeadditionalconditio…
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| 关 键 词： | 单调系统 ANORDER递增 不变量函数 平衡性 收敛性 |
| 收稿时间： | 1993/10/9 0:00:00 |
TYPE K MONOTONE SYSTEMS WITH AN ORDER-INCREASING INVARIANT FUNCTION |
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| Jiang Jifa.TYPE K MONOTONE SYSTEMS WITH AN ORDER-INCREASING INVARIANT FUNCTION[J].Chinese Annals of Mathematics,Series B,1996,17(3):335-342. |
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| Authors: | Jiang Jifa |
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| Institution: | DepartmentofMathematics,TheUniversityofScienceandTechnologyofChina,Hefei230036,China. |
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| Abstract: | The author considers the asymptotic behavior of solutions of a
class of ordinary differential equations $\dot x=F(x)$ in the
nonnegative orthant $\R_+^n.$ Suppose that $F(0)=0, \ F_i(x_1,
\cdots, x_n)$ is nondecreasing in $x_k$ for all $k\not= i$ and
that $F$ possesses an order-increasing invariant function. Then
it is shown that every bounded solution to such a system
converges to a single equilibrium. |
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| Keywords: | Type K monotone system Monotone flow Invariant function Equilibrium Convergence |
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