Related papers: Tune the topology to create or destroy patterns
Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…
Given a reaction-diffusion system interacting via a complex network, we propose two different techniques to modify the network topology while preserving its dynamical behaviour. In the region of parameters where the homogeneous solution…
Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…
The influence of networks topology on collective properties of dynamical systems defined upon it is studied in the thermodynamic limit. A network model construction scheme is proposed where the number of links, the average eccentricity and…
The theory of pattern formation in reaction-diffusion systems is extended to the case of a directed network. Due to the structure of the network Laplacian of the scrutinised system, the dispersion relation has both real and imaginary parts,…
Dynamical processes on networks are currently being considered in different domains of cross-disciplinary interest. Reaction-diffusion systems hosted on directed graphs are in particular relevant for their widespread applications, from…
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…
We study the network reconstruction problem for an epidemic reaction-diffusion. These models are an extension of deterministic, compartmental models to a graph setting, where the reactions within the nodes are coupled by a diffusion. We…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
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…
The ability to reroute and control flow is vital to the function of venation networks across a wide range of organisms. By modifying individual edges in these networks, either by adjusting edge conductances or creating and destroying edges,…
The network of interactions in complex systems, strongly influences their resilience, the system capability to resist to external perturbations or structural damages and to promptly recover thereafter. The phenomenon manifests itself in…
We study diffusion-driven pattern-formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing…
We study the effect of topology variation on the dynamic behavior of a system with local update rules. We implement one-dimensional binary cellular automata on graphs with various topologies by formulating two sets of degree-dependent…
Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is…
Molecular networks guide the biochemistry of a living cell on multiple levels: its metabolic and signalling pathways are shaped by the network of interacting proteins, whose production, in turn, is controlled by the genetic regulatory…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…
Although it is unambiguously agreed that structure plays a fundamental role in shaping the dynamics of complex systems, this intricate relationship still remains unclear. We investigate a general computational transformation by which we can…
A general scheme is proposed and tested to control the symmetry breaking instability of a homogeneous solution of a spatially extended multispecies model, defined on a network. The inherent discreteness of the space makes it possible to act…
The process of pattern formation for a multi-species model anchored on a time varying network is studied. A non homogeneous perturbation superposed to an homogeneous stable fixed point can amplify, as follows a novel mechanism of…