Related papers: Turing instability and pattern formation on direct…
Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…
A new class of patterns for multiplex networks is studied, which consists in a collection of different homogeneous states each referred to a distinct layer. The associated stability diagram exhibits a tricritical point, as a function of the…
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…
Motivated by bacterial chemotaxis and multi-species ecological interactions in heterogeneous environments, we study a general one-dimensional reaction-cross-diffusion system in the presence of spatial heterogeneity in both transport and…
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…
This brief proposes a distributed formation control strategy via matrix-weighted Laplacian that can achieve a similar formation in 2-D planar using inter-agent relative displacement measurement. Formation patterns that include translation,…
Pattern formation in reaction-diffusion systems where the diffusion terms correspond to a Sturm-Liouville problem are studied. These correspond to a problem where the diffusion coefficient depends on the spatial variable: $\nabla \cdot…
As proposed by Alan Turing in 1952 as a ubiquitous mechanism for nonequilibrium pattern formation, diffusional effects may destabilize uniform distributions of reacting chemical species and lead to both spatially and temporally…
We study the discrete Gierer-Meinhardt model of reaction-diffusion on three different types of networks: regular, random and scale-free. The model dynamics lead to the formation of stationary Turing patterns in the steady state in certain…
The stable functionality of networked systems is a hallmark of their natural ability to coordinate between their multiple interacting components. Yet, strikingly, real-world networks seem random and highly irregular, apparently lacking any…
We developed a novel statistical method to identify structural differences between networks characterized by structural equation models. We propose to reparameterize the model to separate the differential structures from common structures,…
We reduce complex stripped patterns to a basic topological network of edges and vertices to define defects and measure their influence on the pattern. We present statistics on the spatial and temporal distribution of defects within the…
This work targets the influence of disorder on the relaxed structure and macroscopic mechanical properties of elastic networks. We construct network classes of different types of disorder (length, topology and stiffness), which are…
The Laplacian matrix and its pseudo-inverse for a strongly connected directed graph is fundamental in computing many properties of a directed graph. Examples include random-walk centrality and betweenness measures, average hitting and…
By discretising space into compartments and letting system dynamics be governed by the reaction-diffusion master equation, it is possible to derive and simulate a stochastic model of reaction and diffusion on an arbitrary domain. However,…
We present theoretical and experimental studies on pattern formation with bistable dynamical units coupled in a star network configuration. By applying a localized perturbation to the central or the peripheral elements, we demonstrate the…
We study the effects of nonreciprocity and network structure on percolation. To this end, we investigate nonreciprocal random networks - directed networks for which the probability of a link occurring from node i to node j differs from the…
We compare spot patterns generated by Turing mechanisms with those generated by replication cascades, in a model one-dimensional reaction-diffusion system. We determine the stability region of spot solutions in parameter space as a function…
We study the time scales associated to diffusion processes that take place on multiplex networks, i.e. on a set of networks linked through interconnected layers. To this end, we propose the construction of a supra-Laplacian matrix, which…
Under suitable assumptions, the dynamic behaviour of a chemical reaction network is governed by an autonomous set of polynomial ordinary differential equations over continuous variables representing the concentrations of the reactant…