Related papers: Turing instabilities from a limit cycle
In geophysical and plasma contexts, zonal flows are well known to arise out of turbulence. We elucidate the transition from statistically homogeneous turbulence without zonal flows to statistically inhomogeneous turbulence with steady zonal…
We demonstrate that the space-time statistics of the birth of turbulent spots in boundary layers can be reconstructed qualitatively from the average behavior of macroscopic measures in the transition zone. The conclusion in \cite{vg04} that…
In this work we suggest that a turbulent phase of the Rayleigh-Taylor instability can be explained as a universal stochastic wave traveling with constant speed in a properly renormalized system. This wave, originating from ordinary…
A new statistical approach is presented to study the thermal instability process of optically thin unmagnetized plasma. In this approach the time evolution of mass distribution function over temperature is calculated. This function…
In recent works, we proposed a hypothesis, according to which turbulence in gases is created by the mean field effect of an intermolecular potential. We discovered that, in a numerically simulated inertial flow, turbulent solutions indeed…
Empirical diagnosis of stability has received considerable attention, mostly focused on variance metrics for early warning signals of abrupt system change. Despite this, the theoretical foundation and application has been limited to…
We describe the resulting spatiotemporal dynamics when a homogeneous equilibrium loses stability in a spatially extended system. More precisely, we consider reaction-diffusion systems, assuming only that the reaction kinetics undergo a…
We investigate the linear instability of flows that are stable according to Rayleigh's criterion for rotating fluids. Using Taylor-Couette flow as a primary test case, we develop large Reynolds number matched asymptotic expansion theories.…
Effect of external periodic force on an oscillatory order in a reaction diffusion system (Gierer Meinhardt model) has been investigated. The 2:1 resonance situation is found susceptible for the generation of a band of phase instabilities.…
We study the convective instability of the melt during the initial transient in a directional solidification experiment in a vertical configuration. We obtain analytically the dispersion relation, and perform an additional asymptotic…
The synchronous dynamics of an array of excitable oscillators, coupled via a generic graph, is studied. Non homogeneous perturbations can grow and destroy synchrony, via a self-consistent instability which is solely instigated by the…
A noisy damping parameter in the equation of motion of a nonlinear oscillator renders the fixed point of the system unstable when the amplitude of the noise is sufficiently large. However, the stability diagram of the system can not be…
Alan Turing's work in Morphogenesis has received wide attention during the past 60 years. The central idea behind his theory is that two chemically interacting diffusible substances are able to generate stable spatial patterns, provided…
Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle,…
Self-oscillations are the result of an efficient mechanism generating periodic motion from a constant power source. In quantum devices, these oscillations may arise due to the interaction between single electron dynamics and mechanical…
The spontaneous emergence of ordered structures, known as Turing patterns, in complex networks is a phenomenon that holds potential applications across diverse scientific fields, including biology, chemistry, and physics. Here, we present a…
The population model of Busenberg and Travis is a paradigmatic model in ecology and tumour modelling due to its ability to capture interesting phenomena like the segregation of populations. Its singular mathematical structure enforces the…
Structure formation in turbulence is effectively an instability of "plasma" formed by fluctuations serving as particles. These "particles" are quantumlike; namely, their wavelengths are non-negligible compared to the sizes of background…
Reaction-diffusion (Turing) systems are fundamental to the formation of spatial patterns in nature and engineering. These systems are governed by a set of non-linear partial differential equations containing parameters that determine the…
Whereas the importance of transient dynamics to the functionality and management of complex systems has been increasingly recognized, most of the studies are based on models. Yet in realistic situations the models are often unknown and what…