Tune the topology to create or destroy patterns

  title={Tune the topology to create or destroy patterns},
  author={Malbor Asllani and Timot{\'e}o Carletti and Duccio Fanelli},
  journal={The European Physical Journal B},
Abstract We consider the dynamics of a reaction-diffusion system on a multigraph. The species share the same set of nodes but can access different links to explore the embedding spatial support. By acting on the topology of the networks we can control the ability of the system to self-organise in macroscopic patterns, emerging as a symmetry breaking instability of an homogeneous fixed point. Two different cases study are considered: on the one side, we produce a global modification of the… 
Topological stabilization for synchronized dynamics on networks
Abstract 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
Amplitude death and restoration in networks of oscillators with random-walk diffusion
Systems composed of reactive particles diffusing in a network display emergent dynamics. While Fick’s diffusion can lead to Turing patterns, other diffusion schemes might display more complex
Turing patterns mediated by network topology in homogeneous active systems.
It is demonstrated that networks with large degree fluctuations tend to have stable patterns over the space of initial perturbations, whereas patterns in more homogenous networks are purely stochastic, and the Turing instability can be induced in any network topology by tuning the diffusion of the competing species or by altering network connectivity.
Turing Instability and Pattern Formation on Directed Networks
  • J. Ritchie
  • Computer Science, Mathematics
    SSRN Electronic Journal
  • 2022
This work addresses the question “how does one detect pattern formation if the Laplacian matrix is not diagonalizable” and addresses the related problem of pattern formation arising from systems of reaction-diffusion equations with non-local (global) reaction kinetics.
Dynamical systems on hypergraphs
Turing patterns and the synchronisation of non linear (regular and chaotic) oscillators are studied, for a general class of systems evolving on hypergraphs.
Delay-induced patterns in a reaction–diffusion system on complex networks
The evolution process of the prey density is revealed and the thick-tailed phenomenon in large-time delay cases is discovered and it is unveiled that the connectivity structures of networks hardly have impact on the trend of evolutionary processes.
A theory of pattern formation for reaction–diffusion systems on temporal networks
Networks have become ubiquitous in the modern scientific literature, with recent work directed at understanding ‘temporal networks’—those networks having structure or topology which evolves over
Percolation and Internet Science
This review presents a model of opinion spreading, the role of the topology of the network to induce coherent oscillations and the influence of risk perception for stopping epidemics, and introduces the open problem of controlling percolation and other processes on distributed systems.
Optimal control of networked reaction–diffusion systems
This work presents a solution to the problem of controlling a reaction–diffusion system in a network to obtain a particular pattern, in the form of an analytical framework and numerical algorithm for optimal control of Turing patterns in networks.
Cross-diffusion-induced patterns in an SIR epidemic model on complex networks.
A linear analysis method is used to study Turing instability induced by cross-diffusion for a network organized SIR epidemic model and explore Turing patterns on several different networks.


The theory of pattern formation on directed networks.
The theory of pattern formation in reaction-diffusion systems defined on symmetric networks is extended to the case of directed networks, which are found in a number of different fields, such as neuroscience, computer networks and traffic systems.
Turing patterns in multiplex networks.
The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The interlayer diffusion constants act as a small parameter
The physics of spreading processes in multilayer networks
Progress is surveyed towards attaining a deeper understanding of spreading processes on multilayer networks, and some of the physical phenomena related to spreading processes that emerge from multilayered structure are highlighted.
Collective dynamics of ‘small-world’ networks
Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.
Pattern formation in multiplex networks
The theory demonstrates that the existence of such topology-driven instabilities is generic in multiplex networks, providing a new mechanism of pattern formation.
Approximating spectral impact of structural perturbations in large networks.
A theory for estimating the change of the largest eigenvalue of the adjacency matrix or the extreme eigenvalues of the graph Laplacian when small but arbitrary set of links are added or removed from the network is developed.
Controllability of complex networks
Analytical tools are developed to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependent control that can guide the system’s entire dynamics.
Localized Patterns in Reaction-Diffusion Systems
A new chemical pattern is discussed, which is a propagationless solitary island in an infinite medium. We demonstrate analytically its existence and stability for a certain simple model. The
Laplacian spectra as a diagnostic tool for network structure and dynamics.
The effects of clustering, degree distribution, and a particular type of coupling asymmetry (input normalization), all of which are known to have effects on the synchronizability of oscillator networks, are studied.