Related papers: A rate-induced tipping in the Pearson diffusion
In this work we study the effect of density dependent nonlinear diffusion on pattern formation in the Lengyel--Epstein system. Via the linear stability analysis we determine both the Turing and the Hopf instability boundaries and we show…
The possibility of rate-induced tipping (R-tipping) away from an attracting fixed point has been thoroughly explored in 1-dimensional systems. In these systems, it is impossible to have R-tipping away from a path of quasi-stable equilibria…
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…
Critical transitions describe sudden changes in the state of an ecosystem. In classical bifurcation theory, such transitions occur when the value of a parameter exceeds a threshold (``bifurcation") value. More recently, critical transitions…
In certain biological contexts, such as the plumage patterns of birds and stripes on certain species of fishes, pattern formation takes place behind a so-called "wave of competency". Currently, the effects of a wave of competency on the…
A habitat that is moving due to environmental change may result in tipping to extinction if the rate at which it moves is too great. We use a scalar reaction-diffusion equation with a non-autonomous reaction term, representing a spatially…
The paper addresses the problem of calculating the noise-induced switching rates in systems with delay-distributed kernels and Gaussian noise. A general variational formulation for the switching rate is derived for any distribution kernel,…
Slow parameter drift is common in many systems (e.g., the amount of greenhouse gases in the terrestrial atmosphere is increasing). In such situations, the attractor on which the system trajectory lies can be destroyed, and the trajectory…
Rogue waves are an intriguing nonlinear phenomenon arising across different scales, ranging from ocean waves through optics to Bose-Einstein condensates. We describe the emergence of rogue-like wave dynamics in a reaction-diffusion system…
We investigate violations of the fluctuation-dissipation theorem in two classes of trap models by studying the influence of the perturbing field on the transition rates. We show that for perturbed rates depending upon the value of the…
The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of…
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…
This paper investigates the exit-time problem for time-inhomogeneous diffusion processes. The focus is on the small-noise behavior of the exit time from a bounded positively invariant domain. We demonstrate that, when the drift and…
Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the…
This paper is concerned with stochastic reaction-diffusion kinetics governed by the reaction-diffusion master equation. Specifically, the primary goal of this paper is to provide a mechanistic basis of Turing pattern formation that is…
We study diffusion-controlled processes in nonequilibrium steady states, where standard rate theory assumptions break down. Using transition path theory, we generalize the relations between reactive probability fluxes and measures of the…
Point processes often have a natural interpretation with respect to a continuous process. We propose a point process construction that describes arrival time observations in terms of the state of a latent diffusion process. In this…
This paper explores the classification of parameter spaces for reaction-diffusion systems of two chemical species on stationary domains. The dynamics of the system are explored both in the absence and presence of diffusion. The parameter…
Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical…
In their way to/from turbulence, plane wall-bounded flows display an interesting transitional regime where laminar and turbulent oblique bands alternate, the origin of which is still mysterious. In line with Barkley's recent work about the…