1k citations · 4k across the 118 of their papers we have counts for
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Random Walks Across Dimensions: Exploring Simplicial Complexes
Diego Febbe, Duccio Fanelli, Timoteo Carletti
We introduce a novel operator to describe a random walk process on a simplicial complex. Walkers are allowed to wonder across simplices of various dimensions, bridging nodes to edg…
Theory of synchronisation and pattern formation on time varying networks
Timoteo Carletti, Duccio Fanelli
Synchronisation and pattern formation have been intensely addressed for systems evolving on static networks. Extending the study to include the inherent ability of the network to a…
Prestrain-induced contraction in 1D random elastic chains
Ihusan Adam, Franco Bagnoli, Duccio Fanelli +2
Prestrained elastic networks arise in a number of biological and technological systems ranging from the cytoskeleton of cells to tensegrity structures. To understand the response o…
Dynamical systems on hypergraphs
Timoteo Carletti, Duccio Fanelli
We present a general framework that enables one to model high-order interaction among entangled dynamical systems, via hypergraphs. Several relevant processes can be ideally traced…
Random walks and community detection in hypergraphs
Timoteo Carletti, Duccio Fanelli, Renaud Lambiotte
We propose a one parameter family of random walk processes on hypergraphs, where a parameter biases the dynamics of the walker towards hyperedges of low or high cardinality. We sho…
Nonlinear walkers and efficient exploration of congested networks
Timoteo Carletti, Malbor Asllani, Duccio Fanelli +1
Random walks are the simplest way to explore or search a graph, and have revealed a very useful tool to investigate and characterize the structural properties of complex networks f…
Generating directed networks with prescribed Laplacian spectra
Sara Nicoletti, Timoteo Carletti, Duccio Fanelli +2
Complex real-world phenomena are often modeled as dynamical systems on networks. In many cases of interest, the spectrum of the underlying graph Laplacian sets the system stability…
Non normal amplification of stochastic quasi-cycles
Sara Nicoletti, Niccolò Zagli, Duccio Fanelli +3
Stochastic quasi-cycles for a two species model of the excitatory-inhibitory type, arranged on a triangular loop, are studied. By increasing the strength of the inter-nodes couplin…
Spectral control for ecological stability
Giulia Cencetti, Franco Bagnoli, Giorgio Battistelli +2
A system made up of N interacting species is considered. Self-reaction terms are assumed of the logistic type. Pairwise interactions take place among species according to different…
Coarse-grained patterns in multiplex networks
Daniel M. Busiello, Timoteo Carletti, Duccio Fanelli
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 stabilit…
Hopping in the crowd to unveil network topology
Malbor Asllani, Timoteo Carletti, Francesca Di Patti +2
We introduce a nonlinear operator to model diffusion on a complex undirected network under crowded conditions. We show that the asymptotic distribution of diffusing agents is a non…
The theory of Turing patterns on time varying networks
Julien Petit, Ben Lauwens, Duccio Fanelli +1
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 p…
Ginzburg-Landau approximation for self-sustained oscillators weakly coupled on complex directed graphs
Francesca Di Patti, Duccio Fanelli, Filippo Miele +1
A normal form approximation for the evolution of a reaction-diffusion system hosted on a directed graph is derived, in the vicinity of a supercritical Hopf bifurcation. Weak diffus…
Global topological control for synchronized dynamics on networks
Giulia Cencetti, Franco Bagnoli, Giorgio Battistelli +3
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…
Benjamin-Feir instabilities on directed networks
Francesca Di Patti, Duccio Fanelli, Filippo Miele +1
The Complex Ginzburg-Landau equation is studied assuming a directed network of coupled oscillators. The asymmetry makes the spectrum of the Laplacian operator complex, and it is ul…
Suppressing escape events in maps of the unit interval with demographic noise
César Parra-Rojas, Joseph D. Challenger, Duccio Fanelli +1
We explore the properties of discrete-time stochastic processes with a bounded state space, whose deterministic limit is given by a map of the unit interval. We find that, in the m…
Tune the topology to create or destroy patterns
Malbor Asllani, Timoteo Carletti, Duccio Fanelli
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 sup…
Pattern formation in a two-component reaction-diffusion system with delayed processes on a network
Julien Petit, Malbor Asllani, Duccio Fanelli +2
Reaction-diffusion systems with time-delay defined on complex networks have been studied in the framework of the emergence of Turing instabilities. The use of the Lambert W-functio…
WKB versus generalized van Kampen system-size expansion: the stochastic logistic equation
Claudia Cianci, Duccio Fanelli, Alan J. McKane
Stochastic fluctuations are central to the understanding of extinction dynamics. In the context of population models they allow for the description of the transition from the vicin…
Multiple scale theory of topology driven pattern on directed networks
Silvia Contemori, Francesca Di Patti, Duccio Fanelli +1
Dynamical processes on networks are currently being considered in different domains of cross-disciplinary interest. Reaction-diffusion systems hosted on directed graphs are in part…
Generalized maximum entropy approach to quasi-stationary states in long range systems
Gabriele Martelloni, Gianluca Martelloni, Pierre de Buyl +1
Systems with long-range interactions display a short-time relaxation towards Quasi Stationary States (QSS) whose lifetime increases with the system size. In the paradigmatic Hamilt…
Delay induced Turing-like waves for one species reaction-diffusion model on a network
Julien Petit, Timoteo Carletti, Mabor Asslani +1
A one species time-delay reaction-diffusion system defined on a complex networks is studied. Travelling waves are predicted to occur as follows a symmetry breaking instability of a…
Emergence of a collective crystal in a classical system with long-range interactions
Alessio Turchi, Duccio Fanelli, Xavier Leoncini
A one-dimensional long-range model of classical rotators with an extended degree of complexity, as compared to paradigmatic long-range systems, is introduced and studied. Working a…
Pattern formation for reactive species undergoing anisotropic diffusion
Daniel M. Busiello, Gwendoline Planchon, Malbor Asllani +2
Turing instabilities for a two species reaction-diffusion systems is studied under anisotropic diffusion. More specifically, the diffusion constants which characterize the ability…