Related papers: Target Patterns in a 2-D Array of Oscillators with…
We consider non-stationary oscillations of an infinite string with time-varying tension. The string lies on the Winkler foundation with a point inhomogeneity (a concentrated spring of negative stiffness). In such a system with constant…
The present investigation deals with the dynamics of a two-degrees-of-freedom system which consists of a main linear oscillator and a strongly nonlinear absorber with small mass. The nonlinear oscillator has a softening hysteretic…
We consider a nonlocal evolution equation representing the continuum limit of a large ensemble of interacting particles on graphs forced by noise. The two principle ingredients of the continuum model are a nonlocal term and Q-Wiener process…
The influence of topological defects on phase synchronization and phase coherence in two-dimensional arrays of locally-coupled, nonidentical, chaotic oscillators is investigated. The motion of topological defects leads to a breakdown of…
We study a nonlocal Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects and degenerate mobility. The nonlocality is described by means of a symmetric singular kernel. We define a notion of weak solution adapted to…
Localization of normal modes is used in recent microelectromechanical systems (MEMS) technologies with orders of magnitude improvements in sensitivity. A pair of eigenvalues veer, or avoid crossing each other, as a single parameter of a…
We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise. Each particle is subjected to a bistable local potential, to a linear coupling with its nearest neighbours, and to an independent…
The main goal of this article is to study a Calder\'on type inverse problem for certain viscous nonlocal wave equations. We show that the partial Dirichlet to Neumann map uniquely determines on the one hand linear perturbations and on the…
We study the homogenization of a class of non-local functionals featuring a rapidly oscillating periodic weight. By means of two-scale convergence, we explicitly evaluate the {\Gamma}-limit for constant target functions, revealing how the…
The linear response is studied in globally coupled oscillator systems including the Kuramoto model. We develop a linear response theory which can be applied to systems whose coupling functions are generic. Based on the theory, we examine…
We consider an abstract second order linear equation with a strong dissipation, namely a friction term which depends on a power of the "elastic" operator. In the homogeneous case, we investigate the phase spaces in which the initial value…
Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are…
We report on existence and properties of discrete gap solitons in zigzag arrays of alternating waveguides with positive and negative refractive indices. Zigzag quasi-one-dimensional configuration of waveguide array introduces strong…
Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear diffusion equations and prove convergence of the method…
We report an interesting symmetry-breaking transition in coupled identical oscillators, namely the continuous transition from homogeneous to inhomogeneous limit cycle oscillations. The observed transition is the oscillatory analog of the…
We develop a framework for localized source detection in dynamical systems governed by nonlinear partial differential equations based on first and second-order sensitivity analysis. Building on the standard adjoint formulation, which…
We consider an extension of Kuramoto's model of coupled phase oscillators where oscillator pairs interact with different strengths. When the coupling coefficient of each pair can be separated into two different factors, each one associated…
In this work, we study the pattern solutions of doubly nonlocal logistic map that include spatial kernels in both growth and competition terms. We show that this map includes as a particular case the nonlocal Fisher-Kolmogorov equation, and…
We develop tools for the analysis of fronts, pulses, and wave trains in spatially extended systems with nonlocal coupling. We first determine Fredholm properties of linear operators, thereby identifying pointwise invertibility of the…
We have investigated synchronized pattern in a network of Thomas oscillators coupled with sinusoidal nonlinear coupling. Pattern like chimera states are not only observed for many non-locally coupled oscillators but there is a signature of…