Related papers: A new dimension to Turing patterns
This study investigates transient wave dynamics in Turing pattern formation, focusing on waves emerging from localised disturbances. While the traditional focus of diffusion-driven instability has primarily centred on stationary solutions,…
Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability…
Turing patterns are a cornerstone of biological self-organization, yet their emergence typically requires finely tuned parameters occupying narrow regions of high-dimensional space. This poses a fundamental challenge: how can evolving…
The concept of Turing instability, namely that diffusion can destabilize the uniform steady state, is well known either in the context of partial differential equations (PDEs) or in networks of dynamical systems. Recently reaction-diffusion…
A growing body of research indicates that structural plasticity mechanisms are crucial for learning and memory consolidation. Starting from a simple phenomenological model, we exploit a mean-field approach to develop a theoretical framework…
We study pattern formation in a chemotaxis model of bacteria and soil carbon dynamics as an example system where transient dynamics can give rise to pattern formation outside of Turing unstable regimes. We use a detailed analysis of the…
The aim of this work is to study the effect of diffusion on the stability of the equilibria in a general two-components reaction-diffusion system with Neumann boundary conditions in the space of continuous functions. As by product, we…
We set up a rigorous thermodynamic description of reaction-diffusion systems driven out of equilibrium by time-dependent space-distributed chemostats. Building on the assumption of local equilibrium, nonequilibrium thermodynamic potentials…
The advances in understanding complex networks have generated increasing interest in dynamical processes occurring on them. Pattern formation in activator-inhibitor systems has been studied in networks, revealing differences from the…
Biological, physical, medical, and numerical applications involving membrane problems on different scales are numerous. We propose an extension of the standard Turing theory to the case of two domains separated by a permeable membrane. To…
In his 1952 paper "The chemical basis of morphogenesis", Alan M. Turing presented a model for the formation of skin patterns. While it took several decades, the model has been validated by finding corresponding natural phenomena, e.g. in…
In his seminal paper on morphogenesis (1952), Alan Turing demonstrated that different spatio-temporal patterns can arise due to instability of the homogeneous state in reaction-diffusion systems, but at least two species are necessary to…
Signaling molecules play an important role for many cellular functions. We investigate here a general system of two membrane reaction-diffusion equations coupled to a diffusion equation inside the cell by a Robin-type boundary condition and…
We show that the Turing patterns in reaction systems with subdiffusion can be replicated in an effective system with Markovian cross-diffusion. The effective system has the same Turing instability as the original system, and the same…
This paper investigates pattern formation in reaction--diffusion systems with both diffusive and nondiffusive components, providing necessary and sufficient conditions for diffusion-driven instability (DDI) and establishing the existence of…
A crucial step in the early development of multicellular organisms involves the establishment of spatial patterns of gene expression which later direct proliferating cells to take on different cell fates. These patterns enable the cells to…
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…
We have studied the entropy-driven mechanism leading to stationary patterns formation in stochastic systems with local dynamics and non-Fickian diffusion. We have shown that a multiplicative noise fulfilling a fluctuation-dissipation…
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…
Turing inspired a computer metaphor of the mind and brain that has been handy and has spawned decades of empirical investigation, but he did much more and offered behavioral and cognitive sciences another metaphor--that of the cascade. The…