Related papers: Turing patterns on networks
In this paper, the Turing instability in reaction-diffusion models defined on complex networks is studied. Here, we focus on three types of models which generate complex networks, i.e. the Erd\H{o}s-R\'enyi, the Watts-Strogatz, and 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…
The problem of pattern formation in a generic two species reaction--diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by…
We hereby develop the theory of Turing instability for reaction-diffusion systems defined on m-directed hypergraphs, the latter being generalization of hypergraphs where nodes forming hyperedges can be shared into two disjoint sets, the…
Reaction-diffusion processes on networked systems have received mounting attention in the past two decades, and the corresponding theory of network dynamics has been continuously enriched with the advancement of network science. Recently,…
The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The intra-layer diffusion constants act as small parameter in the expansion and the unperturbed state…
Long after Turing's seminal Reaction-Diffusion (RD) model, the elegance of his fundamental equations alleviated much of the skepticism surrounding pattern formation. Though Turing model is a simplification and an idealization, it is one of…
Laminar-turbulent pattern formation is a distinctive feature of the intermittency regime in subcritical plane shear flows. By performing extensive numerical simulations of the plane channel flow, we show that the pattern emerges from a…
The problem of Turing instabilities for a reaction-diffusion system defined on a complex Cartesian product networks is considered. To this end we operate in the linear regime and expand the time dependent perturbation on a basis formed by…
Elucidating the neurophysiological mechanisms underlying neural pattern formation remains an outstanding challenge in Computational Neuroscience. In this paper, we address the issue of understanding the emergence of neural patterns by…
Self-organization in natural and engineered systems causes the emergence of ordered spatio-temporal motifs. In presence of diffusive species, Turing theory has been widely used to understand the formation of such patterns on continuous…
Pattern formation in clouds is a well-known feature, which can be observed almost every day. However, the guiding processes for structure formation are mostly unknown, and also theoretical investigations of cloud patterns are quite rare.…
The Turing instability paradigm is revisited in the context of a multispecies diffusion scheme derived from a self-consistent microscopic formulation. The analysis is developed with reference to the case of two species. These latter share…
Diffusion-driven instability and bifurcation analysis are studied in a predator-prey model with herd behavior and quadratic mortality by incorporating multiple Allee effect into prey species. The existence and stability of the equilibria of…
Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the…
Turing's theory of pattern formation is a universal model for self-organization, applicable to many systems in physics, chemistry and biology. Essential properties of a Turing system, such as the conditions for the existence of patterns and…
Confirming Turing's theory of morphogens in developmental processes is challenging, and synthetic biology has opened new avenues for testing Turing's predictions. Synthetic mammalian pattern formation has been recently achieved through a…
Spatial patterns arising spontaneously due to internal processes are ubiquitous in nature, varying from regular patterns of dryland vegetation to complex structures of bacterial colonies. Many of these patterns can be explained in the…
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…
In this work we investigate the effect of density dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability…