Johnson, CharlesMorais, Gonçalo2019-08-292019-08-292019-11-01JOHNSON, Charles; MORAIS, Gonçalo – Bounded domains of negative multipliers. Journal of Mathematical Analysis and Applications. ISSN 0022-247X. Vol. 479, N.º 1 (2019), pp. 926-9400022-247X1096-0813http://hdl.handle.net/10400.21/10435A natural problem associated with coupling of non-autonomous oscillators and synchronization is described. It leads to a question about the boundedness of a domain associated with a derived quadratic form. Properties of real symmetric matrices with bounded domains are developed, and unboundedness is translated into satisfiability of a certain Lyapunov-like matrix form. Eventually the real symmetric matrices associated with unbounded domains are explicitly characterized in terms of inertia explicit matrices. A consequence of the characterization is that large, irreducible matrices are likely to have bounded domains.engInertia explicitLyapunov equationCoupled oscillatorsSynchronizationjournal article10.1016/j.jmaa.2019.06.058