A note on global asymptotic stability of nonautonomous master equations

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October 2013, 18(8): 2143-2149. doi: 10.3934/dcdsb.2013.18.2143

A note on global asymptotic stability of nonautonomous master equations

Christian Lax ^1, and Sebastian Walcher ^2,

1.	Lehrstuhl A für Mathematik, RWTH Aachen, D-52056 Aachen, Germany
2.	Lehrstuhl A für Mathematik, RWTH Aachen, 52056 Aachen

Received March 2013 Revised May 2013 Published July 2013

Abstract
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We present sufficient conditions to either preclude or guarantee global asymptotic stability of linear differential equations for time-dependent $\mathbb W$-matrices. These conditions are concerned with integrability or non-integrability of the matrix entries. The proofs employ differential inequalities.

Keywords: Stability, integrability, convergence, differential inequality., stochastic matrix.

Mathematics Subject Classification: Primary: 34D05, 34D23; Secondary: 37B5.

Citation: Christian Lax, Sebastian Walcher. A note on global asymptotic stability of nonautonomous master equations. Discrete & Continuous Dynamical Systems - B, 2013, 18 (8) : 2143-2149. doi: 10.3934/dcdsb.2013.18.2143

References:

[1]	A. Berman and R. J. Plemmons, "Nonnegative Matrices in the Mathematical Sciences,", Computer Science and Applied Mathematics, (1979). Google Scholar
[2]	B. A. Earnshaw and J. P. Keener, Global asymptotic stability of solutions of nonautonomous master equations,, SIAM J. Applied Dynamical Systems, 9 (2010), 220. doi: 10.1137/090763421. Google Scholar
[3]	N. G. van Kampen, "Stochastic Processes in Physics and Chemistry,", Lecture Notes in Mathematics, 888 (1981). Google Scholar
[4]	W. Walter, "Gewöhnliche Differentialgleichungen,", 7. Aufl., (2000). Google Scholar

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References:

[1]	A. Berman and R. J. Plemmons, "Nonnegative Matrices in the Mathematical Sciences,", Computer Science and Applied Mathematics, (1979). Google Scholar
[2]	B. A. Earnshaw and J. P. Keener, Global asymptotic stability of solutions of nonautonomous master equations,, SIAM J. Applied Dynamical Systems, 9 (2010), 220. doi: 10.1137/090763421. Google Scholar
[3]	N. G. van Kampen, "Stochastic Processes in Physics and Chemistry,", Lecture Notes in Mathematics, 888 (1981). Google Scholar
[4]	W. Walter, "Gewöhnliche Differentialgleichungen,", 7. Aufl., (2000). Google Scholar

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