Related papers: Nonlinear stability of source defects in oscillato…
Planar travelling waves on $\mathbb R^d,$ with $ d\geq 2,$ are shown to persist in systems of reaction-diffusion equations with multiplicative noise on significantly long timescales with high probability, provided that the wave is orbitally…
We derive an equation that governs the spatiotemporal dynamics of small amplitude alternans in paced cardiac tissue. We show that a pattern-forming linear instability leads to the spontaneous formation of stationary or traveling waves whose…
A new dispersion equation is obtained for a non-equilibrium medium with an exponential relaxation model of a vibrationally excited gas. We have researched the dependencies of the pump source and the heat removal on the medium thermodynamic…
Standard model-based control design deteriorates when the system dynamics change during operation. To overcome this challenge, online and adaptive methods have been proposed in the literature. In this work, we consider the class of…
Straightforward method for the derivation of linearized version of stochastic stability analysis of the nonlinear differential equations is presented. Methods for the study of large time behavior of the moments are exposed. These general…
We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and non-uniform stability of the closed-loop system. We apply the…
In this paper, the stability of a dynamically condensing radiative gas layer is investigated by linear analysis. Our own time-dependent, self-similar solutions describing a dynamical condensing radiative gas layer are used as an unperturbed…
Spiral wave propagation in period-2 excitable media is often accompanied by line-defects, the locus of points with period-1 oscillations. Here we investigate spiral line-defects in cardiac tissue where period-2 behavior has a known…
This work is a theoretical investigation of the stability of the non-linear behavior of an oscillating tip-cantilever system used in dynamic force microscopy. Stability criterions are derived that may help to a better understanding of the…
In the previous paper \cite{J1}, we established pointwise bounds for the Green function of the linearized equation associated with spatially periodic traveling waves $\bar u$ of a system of reaction diffusion equations, and also obtained…
We study transmission stabilization of optical solitons against emission of radiation in nonlinear optical waveguides in the presence of weak linear gain-loss, cubic loss, and the collisional Raman frequency shift. We first show how the…
In this paper we consider the spectral and nonlinear stability of periodic traveling wave solutions of a generalized Kuramoto-Sivashinsky equation. In particular, we resolve the long-standing question of nonlinear modulational stability by…
We consider solutions in frequency bands of dispersive equations on the line defined by Fourier multipliers, these solutions being considered as wave packets. In this paper, a refinement of an existing method permitting to expand…
We present a stability theory for kink propagation in chains of coupled oscillators and a new algorithm for the numerical study of kink dynamics. The numerical solutions are computed using an equivalent integral equation instead of a system…
This paper addresses the output regulation problem for a one-dimensional unstable wave equation subject to output delay and all-channel disturbances with unknown frequencies and amplitudes. First, this problem is transformed into a…
The Kuramoto phase diffusion equation is a nonlinear partial differential equation which describes the spatio-temporal evolution of a phase variable in an oscillatory reaction diffusion system. Synchronization manifests itself in a…
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…
A study was made of the instability that arises when acoustic and gravity waves propagate in an inhomogeneous medium which is characterized by oscillatory approach of the reaction coordinates to the steady state. It is shown that loss of…
The purpose of this article is to introduce the original results which devoted with the nonlinear control system problems involves of nonlinear differential equations of fractional orders. Thus, this system is described with a mixed of…
Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering,…