Publications Repository - Helmholtz-Zentrum Dresden-Rossendorf
1 PublicationStabilizing and destabilizing perturbations of PT-symmetric indefinitely damped systems
Kirillov, O.
Eigenvalues of a potential dynamical system with damping forces that are described by an indefinite real symmetric matrix can behave as those of a Hamiltonian system when gain and loss are in a perfect balance. This happens when the indefinitely damped system obeys parity–time (PT ) symmetry. How do pure imaginary eigenvalues of a stable PT -symmetric indefinitely damped system behave when variation in the damping and potential forces destroys the symmetry? We establish that it is essentially the tangent cone to the stability domain at the exceptional point corresponding to the Whitney umbrella singularity on the stability boundary that manages transfer of instability between modes.
Keywords: indefinite damping; PT -symmetry; Krein; signature; dissipation-induced instabilities; exceptional point; modulational instability
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Philosophical Transactions of the Royal Society A 371(2013), 20120051
DOI: 10.1098/rsta.2012.0051
Cited 15 times in Scopus
Permalink: https://www.hzdr.de/publications/Publ-18557
Publ.-Id: 18557