Falsaperla, Paolo and Giacobbe, Andrea and Mulone, Giuseppe (2012) Does symmetry of the operator of a dynamical system help stability? [Journal papers (printed)]
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In this article, we address the question of relating the stability properties of an operator with the stability properties of its associate symmetric operator. The linear-algebra results of Bendixson and Hirsch indicate that the symmetric part of a matrix is always less stable than the matrix itself. We show that in a variety of cases, including infinite dimensional cases associated to systems of PDEs, the same result is valid. We also discuss the applicability to non-autonomous systems, and we show that, in general, this result is not valid. We also review some of the the literature that in these years has appeared on the subject.
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