Analysis of the linear stability of stationary solutions in a circular laser containing a saturable absorber “LSA” for inhomogeneous broadening

In this present paper, the optical bistability in a circular laser containing a saturable absorber LSA for inhomogeneous broadening is studied. A simple mathematical model was developed to describe the action of this type of laser in a circular resonator under two conditions, when the spontaneous emission is neglected or included in the cavity. For both of these two cases, the coefficient of saturation was considered to be equal or different to unity (ζ=1 or ζ≠1). The photons intensities Q_j were determined as function of the pumping rate σ₀ of the active medium and analyzed the linear stability of the stationary solutions obtained in a circular laser containing a saturable absorber “LSA” for inhomogeneous broadening.     

Exploring bistability in rotating Bose-Einstein condensates by a quotient transformation invariant continuation method

We study the discrete nonlinear Schrödinger (DNLS) equations that model rotating Bose-Einstein Condensates (BEC) both analytically and numerically. Due to the difficulties associated with transformation invariant solutions, standard continuation methods may not properly follow the solution curves of the DNLS equations. We propose a quotient transformation invariant continuation method to circumvent this obstacle. We also analyze the bifurcation properties of the primal stalk solution curve corresponding to the DNLS equations for an isotropic trap. In numerical computation, the existence of a bistable region corresponding to the bound states with a 0- or 1-vortex is shown. This finding not only agrees with the physics of the experimental phenomena, but also explains why a 0- or 1-vortex may be observed within a certain region that has an angular velocity. Numerical evidence shows that trap potentials have little effect on the width of the bistable regions. In contrast, intra-component scattering length significantly affects the bistable region.     

Coexistence and bistability of a competition model with mixed dispersal strategy

In this paper, we investigate a Lotka–Volterra competition model with Danckwerts boundary conditions in a one-dimensional habitat where one species assumes pure random diffusion while another one undergoes mixed movement (both random and directed movements). We focus on the joint influence of advection rate, intrinsic growth rate and interspecific competition coefficient on the competition outcomes. It turns out that there exist some critical curves which separate the stable region of the semitrivial steady states from the unstable one. The locations of these curves determine whether coexistence or bistability occurs. More precisely, there are various tradeoffs between advection rate, intrinsic growth rate and interspecific competition coefficient that allow the transition of competition outcomes including competition exclusion, coexistence and bistability. We illustrate our results in various parameter spaces.     

铁在硫酸溶液中活化钝化转移过程的随机共振研究(英文)

本文描述了铁在硫酸中活化 钝化转移过程的双稳特征 ,并模拟出该过程的随机共振现象 .     

Bistability and stationary gap solitons in quasiperiodic photonic crystals based on Thue–Morse sequence

The nonlinear properties of quasiperiodic photonic crystals based on the Thue–Morse sequence are investigated. The intrinsic asymmetry of these one-dimensional structures for odd generation numbers results in bistability thresholds which are sensitive to propagation direction. Along with resonances of perfect transmission, this feature allows to obtain strongly nonreciprocal propagation and to create an all-optical diode. The efficiency of two schemes is compared: passive and active when an additional short pump signal is applied to the system. The existence of stationary gap solitons in quasiperiodic photonic crystals is shown numerically, and their difference from the Bragg case is emphasized.     

Investigation on the bistability of linearly chirped nonlinear Bragg gratings

Based on the nonlinear coupled mode theory, by using the reversely recursive transmission matrix method, the switching characteristics of linearly chirped nonlinear Bragg gratings (LC-NLBG) have been investigated numerically. The results show that, introducing spatial chirp in fiber gratings is helpful to widen the bistable wavelength range, and the influence of the chirp on the switching-on threshold and the on-off ratio of the bistable switching are obvious, the chirp-dependent bistability is due to the difference of the axial distribution of forward wave intensity in the gratings.     

Bifurcation magnetic resonance in films magnetized along hard magnetization axis

We study low-frequency ferromagnetic resonance in a thin film magnetized along the hard magnetization axis performing an analysis of magnetization precession dynamics equations and numerical simulation. Two types of films are considered: polycrystalline uniaxial films and single-crystal films with cubic magnetic anisotropy. An additional (bifurcation) resonance initiated by the bistability, i.e. appearance of two closely spaced equilibrium magnetization states is registered. The modification of dynamic modes provoked by variation of the frequency, amplitude, and magnetic bias value of the ac field is studied. Both steady and chaotic magnetization precession modes are registered in the bifurcation resonance range.     

Stability of a nonlocal delayed reaction–diffusion equation with a non-monotone bistable nonlinearity

The present work is devoted to the stability and attractivity analysis of a nonlocal delayed reaction–diffusion equation (DRDE) with a non-monotone bistable nonlinearity that describes the population dynamics for a two-stage species with Allee effect. By the idea of relating the dynamics of the nonlinear term to the DRDE and some stability results for the monostable case, we describe some basin of attractions for the DRDE. Additionally, existence of heteroclinic orbits and periodic oscillations are also obtained. Numerical simulations are also given at last to verify our theoretical results.     

Propagation of electromagnetic waves through very thin non-Hermitian slabs

A theoretical model is proposed to study the propagation of monochromatic electromagnetic plane waves through very thin slabs having gain or loss. The analysis is based on solving the differential equations directly and applying the appropriate boundary conditions. The optical response of the slabs is considered in the linear and nonlinear regimes with a Kerr-type nonlinearity. A number of relations between the real and imaginary parts of the dielectric function are derived in order that useful effects related to the non-Hermiticity of the system be presented. The transmission of plane waves through a system consisting of two thin slabs satisfying the condition of Parity-Time symmetry is also considered.     

The simple model and linear stability analysis of the electrode process with the NDR region caused by the potential-dependent convective transport

In our earlier report on the experimental studies of convection coupled with electrochemical processes of Hg ions at the mercury electrode we showed that the potential-dependent onset and decay of this convection can give rise to the N-shaped negative differential resistance (NNDR) in the current–potential characteristics. As a consequence, the presence of appropriate serial ohmic resistance in the electric circuit caused bistability. Since the rather poorly reproducible nature of this convection makes the precise experimental studies difficult, we elaborated the simple model which extracts the basic dynamical properties of the system under study. The model involves the electrode potential and the Nernst layer thickness for the convective diffusion as the dynamical variables. Using linear stability analysis we derived the stability criteria and constructed the bifurcation diagram, showing bistability, in accordance with the experimental data, but not predicting the oscillatory behavior.