Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

A note on global asymptotic stability of nonautonomous master equations

Pages: 2143 - 2149, Volume 18, Issue 8, October 2013      doi:10.3934/dcdsb.2013.18.2143

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Christian Lax - Lehrstuhl A für Mathematik, RWTH Aachen, D-52056 Aachen, Germany (email)
Sebastian Walcher - Lehrstuhl A für Mathematik, RWTH Aachen, 52056 Aachen, Germany (email)

Abstract: 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, convergence, stochastic matrix, integrability, differential inequality.
Mathematics Subject Classification:  Primary: 34D05, 34D23; Secondary: 37B55.

Received: March 2013;      Revised: May 2013;      Available Online: July 2013.