Related papers: Instability of Isolated Spectrum for W-shaped Maps
This paper deals with the Sturm-Liouville problem with singular potential of the Sobolev space $W_2^{-1}$ and polynomials of the spectral parameter in a boundary condition. We prove the uniform boundedness and the uniform stability for the…
We study spectral stability of small amplitude periodic traveling waves of the Ostrovsky equation. We prove that these waves exhibit spectral instabilities arising from a collision of pair of non-zero eigenvalues on the imaginary axis when…
The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the…
Energetic astrophysical phenomena, such as $\gamma$-ray bursts, supernova explosions, and magnetar flares occur in collisionless plasmas and involve various plasma kinetic and magnetohydrodynamic instabilities. In this paper, we explore the…
Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…
Experiments observing the liquid surface in a vertically oscillating container have indicated that modeling the dynamics of such systems require maps that admit states at infinity. In this paper we investigate the bifurcations in such a…
In recent work on equiangular lines, Jiang, Tidor, Yuan, Zhang, and Zhao showed that a connected bounded degree graph has sublinear second eigenvalue multiplicity. More generally they show that there cannot be too many eigenvalues near the…
We study regular graphs whose distance-$2$ graph or distance-$1$-or-$2$ graph is strongly regular. We provide a characterization of such graphs $\Gamma$ (among regular graphs with few distinct eigenvalues) in terms of the spectrum and the…
In this paper, we investigate the spectral properties of Andr\'asfai graphs, focusing on key parameters: the second-largest and smallest eigenvalues, the number of distinct eigenvalues, and the multiplicities of the eigenvalues 1 and -1.…
Discrete time evolution of one-dimensional maps is embedded in continuous time by truncating the Taylor series expansion of the time evolution operator to a finite order N. Truncations with N > 4 leads to unconditional instability.…
Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction…
Real magnonic crystals - periodic magnetic media for spin wave (magnon) propagation - may contain some defects. We report theoretical spin wave spectra of a one dimensional magnonic crystal with an isolated defect. The latter is modeled by…
The goal of this work is to determine classes of travelling solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz. It is shown that spurious solitary waves can occur in…
An amplitude equation for an unstable mode in a collisionless plasma is derived from the dynamics on the unstable manifold of the equilibrium $F_0(v)$.\\ The mode eigenvalue arises from a simple zero of the dielectric $\epsilon_{{k}}(z)$;…
We consider the inverse problem of determining the metric-measure structure of collapsing manifolds from local measurements of spectral data. In the part I of the paper, we proved the uniqueness of the inverse problem and a continuity…
The stability and transition in the bottom boundary layer under a solitary wave are analysed in the presence of finite amplitude disturbances. First, the receptivity of the boundary layer is investigated using a linear input-output…
We investigate properties of signed graphs that have few distinct eigenvalues together with a symmetric spectrum. Our main contribution is to determine all signed $(0,2)$-graphs with vertex degree at most $6$ that have precisely two…
We derive the precise stability criterion for smooth solitary waves in the b-family of Camassa-Holm equations. The smooth solitary waves exist on the constant background. In the integrable cases b = 2 and b = 3, we show analytically that…
We address the count of isolated and embedded eigenvalues in a generalized eigenvalue problem defined by two self-adjoint operators with a positive essential spectrum and a finite number of isolated eigenvalues. The generalized eigenvalue…
The general question of how a beam becomes unstable has been one of the fundamental research topics among beam and accelerator physicists for several decades. In this study, we revisited the general problem of linear beam stability in…