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THE ALGEBRAIC CRITERIA FOR THE ASYMPTOTIC BEHAVIOR OF COOPERATIVE SYSTEMS WITH CONCAVE NONLINEARITIES

THE ALGEBRAIC CRITERIA FOR THE ASYMPTOTIC BEHAVIOR OF COOPERATIVE SYSTEMS WITH CONCAVE NONLINEARITIES
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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. 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.
出处 《Systems Science and Mathematical Sciences》 SCIE EI CSCD 1993年第3期193-208,共16页
关键词 Periodic COOPERATIVE systems CONCAVE NONLINEARITIES discrete dynamics of COOPERATIVE CONCAVE MAPS Perron-Frobenius theory Periodic cooperative systems concave nonlinearities discrete dynamics of cooperative concave maps Perron-Frobenius theory
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