Related papers: Synchronization, chaos, and breakdown of collectiv…
We performed an extensive numerical study of a two-dimensional reaction-diffusion system of the activator-inhibitor type in which domain patterns can form. We showed that both multidomain and labyrinthine patterns may form spontaneously as…
The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental…
Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal-mesenchymal coupling in development, and symmetry-breaking in cell polarisation. We develop…
In this letter, we report a numerical study on the collective dynamics of two mutually coupled Thomas oscillators with linear/nonlinear coupling in a dynamic environment. We claim our model calculations can explain the diffusion of…
In coupled reaction-diffusion systems, modes with two different length scales can interact to produce a wide variety of spatiotemporal patterns. Three-wave interactions between these modes can explain the occurrence of spatially complex…
Spatiotemporal chaos in the form of defect-mediated turbulence is known for oscillators coupled by diffusion. Here we explore the same conditions that produce defect turbulence, in an array of oscillators that are coupled through the…
Reaction-diffusion (RD) mechanisms in chemical and biological systems can yield a variety of patterns that may be functionally important. We show that diffusive coupling through the inactivating component in a generic model of coupled…
In this article we introduce an original model in order to study the emergence of chaos in a reaction diffusion system in the presence of self- and cross-diffusion terms. A Fourier Spectral Method is derived to approximate equilibria and…
The Turing instability is a paradigmatic route to patterns formation in reaction-diffusion systems. Following a diffusion-driven instability, homogeneous fixed points can become unstable when subject to external perturbation. As a…
The emergence of stable disordered patterns in reactive system on spatially homogenous substrate is studied in the context of vegetation patterns in the semi-arid climatic zone. It is shown that reaction-diffusion systems that allow for…
Hyperbolic reaction-diffusion equations have recently attracted attention both for their application to a variety of biological and chemical phenomena, and for their distinct features in terms of propagation speed and novel instabilities…
The reaction-diffusion processes in a growing domain involves a dilution term that modifies the properties of the homogeneous state that, in contrast to a fixed domain, depends on time. We study how the dilution term changes the steady…
Two important classes of spatio-temporal patterns, namely, spatio-temporal chaos and self-replicating patterns, for a representative three variable autocatalytic reaction mechanism coupled with diffusion has been studied. The…
We report experimental evidence of the route to spatiotemporal chaos in a large 1D-array of hotspots in a thermoconvective system. Increasing the driving force, a stationary cellular pattern becomes unstable towards a mixed pattern of…
In this paper, we propose a framework to investigate the collective dynamics in ensembles of globally coupled phase oscillators when higher-order modes dominate the coupling. The spatiotemporal properties of the attractors in various…
We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of…
Synchronization transition in oscillatory networks manifests itself as the appearance of a periodic global mode. While perfect in the thermodynamic limit, this mode fluctuates for finite ensembles. We characterize the coherence of this mode…
General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns with…
Spontaneous rhythmic oscillations are widely observed in various real-world systems. In particular, biological rhythms, which typically arise via synchronization of many self-oscillatory cells, often play important functional roles in…
In a quasi-1D thermal convective system consisting of a large array of nonlinearly coupled oscillators, clustering is the way to achieve a regime of mostly antiphase synchronized oscillators. This regime is characterized by a spatiotemporal…