| THE ALGEBRAIC CRITERIA FOR THE ASYMPTOTIC BEHAVIOR OF COOPERATIVE SYSTEMS WITH CONCAVE NONLINEARITIES |
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| 引用本文： | JIANG Jifa Department of Mathematcs,Anhui Normal University,Wuhu 241000,China. THE ALGEBRAIC CRITERIA FOR THE ASYMPTOTIC BEHAVIOR OF COOPERATIVE SYSTEMS WITH CONCAVE NONLINEARITIES[J]. 系统科学与复杂性, 1993, 0(3) |
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| 作者姓名： | JIANG Jifa Department of Mathematcs Anhui Normal University Wuhu 241000 China |
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| 作者单位： | JIANG Jifa Department of Mathematcs，Anhui Normal University，Wuhu 241000，China |
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| 摘 要： | For the discrete dynamical system on the nonnegative orthant generated bya cooperative and concave map T, we present an algebraic criterion of its asymptoticbehavior. The global behavior of such a system is completely determined by the sign of allprincipal minors of the matrix I-DT(0). This criterion applies to the cooperative systemwhich is concave, time-dependent and periodic in t. We give the sufficient conditions thatthe zero solution of such a system is globally asymptotically stable and that it possesses anonzero periodic solution which attracts all initial conditions in the nonnegative orthant.except at the origin. The results of Smith under weaker conditions and some applicationsare included.
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THE ALGEBRAIC CRITERIA FOR THE ASYMPTOTIC BEHAVIOR OF COOPERATIVE SYSTEMS WITH CONCAVE NONLINEARITIES |
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| JIANG Jifa. THE ALGEBRAIC CRITERIA FOR THE ASYMPTOTIC BEHAVIOR OF COOPERATIVE SYSTEMS WITH CONCAVE NONLINEARITIES[J]. Journal of Systems Science and Complexity, 1993, 0(3) |
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| Authors: | JIANG Jifa |
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| Affiliation: | JIANG Jifa Department of Mathematcs,Anhui Normal University,Wuhu 241000,China |
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| Abstract: | For the discrete dynamical system on the nonnegative orthant generated bya cooperative and concave map T, we present an algebraic criterion of its asymptoticbehavior. The global behavior of such a system is completely determined by the sign of allprincipal minors of the matrix I-DT(0). This criterion applies to the cooperative systemwhich is concave, time-dependent and periodic in t. We give the sufficient conditions thatthe zero solution of such a system is globally asymptotically stable and that it possesses anonzero periodic solution which attracts all initial conditions in the nonnegative orthant.except at the origin. The results of Smith under weaker conditions and some applicationsare included. |
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| Keywords: | Periodic cooperative systems concave nonlinearities discrete dynamics of cooperative concave maps Perron-Frobenius theory |
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