Related papers: Phase and frequency linear response theory for hyp…
The phase reduction method for a limit cycle oscillator subjected to a strong amplitude-modulated high-frequency force is developed. An equation for the phase dynamics is derived by introducing a new, effective phase response curve. We show…
We consider a slow-fast Hamiltonian system with one fast angular variable (a fast phase) whose frequency vanishes on some surface in the space of slow variables (a resonant surface). Systems of such form appear in the study of dynamics of…
This study investigates chaotic diffusion in multi-scale turbulence driven by nonlinear wave-particle resonance coupling. Turbulent waves with distinct characteristic wavelengths across scales coherently interact with charged particles when…
Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final…
We present an approach which enables to state about the existence of phase synchronization in coupled chaotic oscillators without having to measure the phase. This is done by observing the oscillators at special times, and analyzing whether…
A nonlinear response theory is provided by use of the transient linearization method in the spatially one-dimensional Vlasov systems. The theory inclusively gives responses to external fields and to perturbations for initial stationary…
The long therm behavior of chaotic flows is investigated by means of time dependent frequency analysis. The system under test consists of an electrically conducting fluid, confined between two differentially rotating spheres. The spherical…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…
We study chemical oscillators in the presence of phase separation. By imposing timescale separation between slow reactions and fast diffusion, we define a dynamics at phase equilibrium for the relevant degrees of freedom. We demonstrate…
Recently, a nonlinear stability theory has been developed for wave trains in reaction-diffusion systems relying on pure $L^\infty$-estimates. In the absence of localization of perturbations, it exploits diffusive decay caused by smoothing…
Sound scattering by a finite width beam on a single rigid body rotation vortex flow is detected by a linear array of transducers (both smaller than a flow cell), and analyzed using a revised scattering theory. Both the phase and amplitude…
We study general linear transport-reaction systems on an arbitrary dimensional hypercube with periodic boundary conditions. Transport-reaction systems are often used to model the finite speed movement and interaction of particles, bacteria…
Self-consistent closure theory for passive-scalar turbulence has been developed on the basis of the Hessian of the scalar field. As a primitive indicator of spatial structure of the scalar, we employ the Hessian into the core of the theory…
A frequency-based omni-temporal dispersion theory is developed to capture the transient interplay between diffusion, advection, and reaction during solute transport through porous media. Unlike classical asymptotic dispersion theories,…
Biological systems can rely on collective formation of a metachronal wave in an ensemble of oscillators for locomotion and for fluid transport. We consider one-dimensional chains of phase oscillators with nearest neighbor interactions,…
In a smooth flow, the leading-order response of trajectories to infinitesimal perturbations in their initial conditions is described by the finite-time Lyapunov exponents and associated characteristic directions of stretching. We give a…
A phase diagram, defined by the amplitude square and phase of scattering coefficients for absorption cross-section in each individual channel, is introduced as a universal map on the electromagnetic properties for passive scatterers.…
The tendency for flows in microfluidic systems to behave linearly poses a challenge for designing integrated flow control schemes to carry out complex fluid processing tasks. This hindrance has led to the use of numerous external control…
The Cahn-Hilliard equation with an externally-prescribed chaotic shear flow is studied in two and three dimensions. The main goal is to compare and contrast the phase separation in two and three dimensions, using high-resolution numerical…