Time-reversal symmetry and pseudo-Hermicity are shown to lead five universal level statistics of real eigenvalues non-Hermitian systems, using random matrix theory analyses numerical diagonalizations.

We consider a class of one-dimensional nonhermitian oscillators and discuss the relationship between the real eigenvalues of PT-symmetric oscillators and the resonances obtained by different authors. We also show the relationship between the strong-coupling expansions for the eigenvalues of those oscillators. Comparison of the results of the complex rotation and the Riccati-Padé methods reveals...

Fluid queueing models with finite capacity buffers are applied to analyze a wide range of real life systems. There are well established numerical procedures for the analysis of these queueing models when the load is lower or higher than the system capacity, but these numerical methods become unstable as the load gets close to the system capacity. One of the available numerical procedures is the...

In the context of the theory of switched systems, and especially of the openloop stabilization problem, it is interesting to study the relationship between the placement of the eigenvalues of a matrix of the form H = θ1A1 + θ2A2 and those of the matrix E = e22e11 . It is well known that if all the eigenvalues of H have negative real part and θ1 + θ2 is small enough, then the eigenvalues of E li...

We consider the persistence and stability of dark solitons in the Gross–Pitaevskii (GP) equation with a small decaying potential. We show that families of black solitons with zero speed originate from extremal points of an appropriately defined effective potential and persist for sufficiently small strength of the potential. We prove that families at the maximum points are generally unstable wi...

The partly symmetric real Ginibre ensemble consists of matrices formed as linear combinations of real symmetric and real anti-symmetric Gaussian random matrices. Such matrices typically have both real and complex eigenvalues. For a fixed number of real eigenvalues, an earlier work has given the explicit form of the joint eigenvalue probability density function. We use this to derive a Pfaffian ...

Stability analysis of linear circuits and systems under interval parameter uncertainties can be equated to estimating the eigenvalues of interval matrices. In this paper, the problem of determining outer bounds on the ranges of the real eigenvalues is considered. A method for computing such bounds is suggested. It consist of setting up and solving a system of n nonlinear equations, n being the ...

Invariant pairs have been proposed as a numerically robust means to represent and compute several eigenvalues along with the corresponding (generalized) eigenvectors for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In this work, we consider nonlinear eigenvalue problems that depend on an additional parameter and our interest is to track several eigenvalues as this ...