Related papers: On a connection between nonstationary and periodic…
We consider a model where a population of diffusively coupled limit-cycle oscillators, described by the complex Ginzburg-Landau equation, interacts nonlocally via an inertial field. For sufficiently high intensity of nonlocal inertial…
In present paper we suggest a new universal approach to study complex systems by microscopic, mesoscopic and macroscopic methods. We discuss new possibilities of extracting information on nonstationarity, unsteadiness and non-Markovity of…
This is a study of two-dimensional steady periodic travelling waves on the surface of an infinitely deep irrotational ocean, when the top streamline is in contact with a membrane which has a nonlinear response to stretching and bending, and…
In systems that exhibit a bistability between nonlinear traveling waves and the basic state, pairs of fronts connecting these two states can form localized wave pulses whose stability depends on the interaction between the fronts. We…
New results concerning the orbital stability of periodic traveling wave solutions for the "abcd" Boussinesq model will be shown in this manuscript. For the existence of solutions, we use basic tools of ordinary differential equations to…
By a refinement of the technique used by Johnson and Zumbrun to show stability under localized perturbations, we show that spectral stability implies nonlinear modulational stability of periodic traveling-wave solutions of reaction…
We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for…
This paper presents a new numerical approach to the study of non-periodicity in signals, which can complement the maximal Lyapunov exponent method for determining chaos transitions of a given dynamical system. The proposed technique is…
Many systems arising in biological applications are subject to periodic forcing. In these systems the forcing parameter is not only time-varying but also known to have a periodic structure. We present an approach to estimating periodic,…
We study nonlinear dynamics of superposition of quantum wavepackets in various systems such as Kerr medium, Morse oscillator and bosonic Josephson junction. The prime reason behind this study is to find out how the superposition of states…
A well-behaved adjoint sensitivity technique for chaotic dynamical systems is presented. The method arises from the specialisation of established variational techniques to the unstable periodic orbits of the system. On such trajectories,…
A method based on wavelet transform and genetic programming is proposed for characterizing and modeling variations at multiple scales in non-stationary time series. The cyclic variations, extracted by wavelets and smoothened by cubic…
We subject the stationary solutions of inviscid and axially symmetric rotational accretion to a time-dependent radial perturbation, which includes nonlinearity to any arbitrary order. Regardless of the order of nonlinearity, the equation of…
Understanding the evolving dependence between two clusters of multivariate signals is fundamental in neuroscience and other domains where sub-networks in a system interact dynamically over time. Despite the growing interest in multivariate…
We outline a general theory for the analysis of flow-distributed standing and travelling wave patterns in one-dimensional, open plug-flows of oscillatory chemical media. We treat both the amplitude and phase dynamics of small and…
We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous multi-scale stochastic system with irregular coefficients,…
Oscillons are localised long-lived pulsating states in the three-dimensional $\phi^4$ theory. We gain insight into the spatio-temporal structure and bifurcation of the oscillons by studying time-periodic solutions in a ball of a finite…
The periodic solutions of a type of nonlinear hyperbolic partial differential equations with a localized nonlinearity are investigated. For instance, these equations are known to describe several acoustical systems with fluid-structure…
The main purpose of the present paper is to investigate the nonlinear stability of viscous shock waves and rarefaction wave for bipolar Vlasov-Poisson-Boltzmann (VPB) system. To this end, motivated by the micro-macro decomposition to the…
In this paper we introduce a notion of a directional uncertainty product for multivariate periodic functions. It measures a localization of a function along a particular direction. We study properties of the uncertainty product and give an…