Related papers: Phase reduction approach to synchronization of spa…
We introduce a simplified technique for incorporating diffusive phenomena into lattice-gas molecular dynamics models. In this method, spatial interactions take place one dimension at a time, with a separate fractional timestep devoted to…
This study solves the output regulation problem for a reaction-diffusion system confronting concurrent input delay and fully unidentified disturbances (encompassing both unknown frequencies and amplitudes) across all channels. The principal…
Rhythmic activity is ubiquitous in biological systems from the cellular to organism level. Reconstructing the instantaneous phase is the first step in analyzing the essential mechanism leading to a synchronization state from the observed…
We introduce here a simple finite-dimensional feedback control scheme for stabilizing solutions of infinite-dimensional dissipative evolution equations, such as reaction-diffusion systems, the Navier-Stokes equations and the…
Reaction-diffusion systems where transition rates exhibit quenched disorder are common in physical and chemical systems. We study pair reactions on a periodic two-dimensional lattice, including continuous deposition and spontaneous…
Reaction-diffusion systems offer a powerful framework for understanding self-organized patterns in biological systems, yet controlling these patterns remains a significant challenge. As a consequence, we present a rigorous framework of…
We propose a method to analytically show the possibility for the appearance of a maximum in the signal-to-noise ratio in nonpotential systems. We apply our results to the FitzHugh-Nagumo model under a periodic external forcing, showing that…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
We present the spatial regime conversion method (SRCM), a novel hybrid modelling framework for simulating reaction-diffusion systems that adaptively combines stochastic discrete and deterministic continuum representations. Extending the…
An approach is presented for coupled chaotic systems, estimating an inferior bound value for the absolute phase difference, in order to say that phase synchronization is present. This approach shows that synchronicity in phase implies…
Rotating spiral waves are a form of self-organization observed in spatially extended systems of physical, chemical, and biological nature. A small perturbation causes gradual change in spatial location of spiral's rotation center and…
We theoretically investigate collective phase synchronization between interacting groups of globally coupled noisy identical phase oscillators exhibiting macroscopic rhythms. Using the phase reduction method, we derive coupled collective…
We introduce a simple model system to study synchronization theoretically in quantum oscillators that are not just in limit-cycle states, but rather display a more complex bistable dynamics. Our oscillator model is purely dissipative, with…
The phase-space of a simple synchronization model is thoroughly investigated. The model considers two-mode stochastic oscillators, coupled through a pulse-like interaction controlled by simple optimization rules. A complex phase space is…
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
We study the dynamics of the quantum phase distribution associated with the reduced density matrix of a system for a number of situations of practical importance, as the system evolves under the influence of its environment, interacting via…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
We consider a spatially extended mesoscopic FitzHugh-Nagumo model with strong local interactions and prove that its asymptotic limit converges towards the classical nonlocal reaction-diffusion FitzHugh-Nagumo system. As the local…
In two-dimensional reaction-diffusion systems, local curvature perturbations in the shape of traveling waves are typically damped out and disappear in the course of time. If, however, the inhibitor diffuses much faster than the activator,…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…