Stability of dynamical systems is a central topic with applications in widespread areas such as economy, biology, physics and mechanical engineering. The dynamics of nonlinear systems may completely change due to perturbations forcing the solution to jump from a safe state into another, possibly dangerous, attractor. Such phenomena can not be traced by the widespread local stability and resilie...

The growth of small perturbations and the temperature correlation function of cosmic background radiation induced by the perturbations in the isotropic and homogeneous universe with arbitrary spatial curvature, filled with nonrelativistic and so-called string-like matter is calculated. It is shown that both magnitudes are insensitive to the eventual existence of the string-like matter in the un...

The cosmic expansion history tests the dynamics of the global evolution of the universe and its energy density contents, while the cosmic growth history tests the evolution of the inhomogeneous part of the energy density. Precision comparison of the two histories can distinguish the nature of the physics responsible for the accelerating cosmic expansion: an additional smooth component – dark en...

in the present work, a hybrid of fourier transform and homotopy perturbation method is developed for solving the non-homogeneous partial differential equations with variable coefficients. the fourier transform is employed with combination of homotopy perturbation method (hpm), the so called fourier transform homotopy perturbation method (fthpm) to solve the partial differential equations. the c...

in this paper, we consider the inhomogeneous time-fractional nonlinear fisher equation with three known boundary conditions. we first apply a modified homotopy perturbation method for translating the proposed problem to a set of linear problems. then we use the separation variables  method to solve obtained problems. in examples, we illustrate that by right choice of source term in the modified...

The growth of the two-dimensional single-mode Rayleigh-Taylor instability (RTI) at low Atwood number (A=0.04) is investigated using Direct Numerical Simulations. The main result of the paper is that, at long times and sufficiently high Reynolds numbers, the bubble acceleration becomes stationary, indicating mean quadratic growth. This is contrary to the general belief that single-mode Rayleigh-...

State-of-the-art deep NLP models have achieved impressive improvements on many tasks. However, they are found to be vulnerable some perturbations. Before widely adopted, the fundamental issues of robustness need addressed. In this paper, we design a enhancement method defend against word substitution perturbation, whose basic idea is fight perturbation with perturbation. We find that: although ...

The dynamics of solitons of the nonlinear Schrödinger equation under the influence of dissipative and dispersive perturbations is investigated. In particular a coupling to a long-wave mode is considered using extended GinzburgLandau equations. The study is motivated by the experimental observation of localized wave trains (‘pulses’) in binary-liquid convection. These pulses have been found to d...