An extension of Morishima’s nonlinear Perron-Frobenius theorem
نویسندگان
چکیده
منابع مشابه
Stochastic Nonlinear Perron-frobenius Theorem∗
We establish a stochastic nonlinear analogue of the PerronFrobenius theorem on eigenvalues and eigenvectors of positive matrices. The result is formulated in terms of an automorphism T of a probability space (Ω,F , P ) and a random mapping D(ω, ·) : R+ → R+. Under assumptions of monotonicity and homogeneity of D(ω, ·), we prove the existence of scalar and vector measurable functions α(ω) > 0 an...
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The spectral radius of a matrix A is the maximum norm of all eigenvalues of A. In previous work we already formalized that for a complex matrix A, the values in A grow polynomially in n if and only if the spectral radius is at most one. One problem with the above characterization is the determination of all complex eigenvalues. In case A contains only non-negative real values, a simplification ...
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This paper deals with homogeneous cooperative sys-terns, a class of positive systems. It is shown that they admit a fairly simple asymptotic behavior, thereby generalizing the well-known Perron-Frobenius theorem from linear to homogeneous systems. As a corollary a simple criterion for global asymptotic stability is established. Then these systems are subject to constant inputs and we prove that...
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ژورنال
عنوان ژورنال: Kyoto Journal of Mathematics
سال: 1983
ISSN: 2156-2261
DOI: 10.1215/kjm/1250521436