318 citations · 2.8k across the 60 of their papers we have counts for
13 papers · 1 filter
Dirac synchronization is rhythmic and explosive
Lucille Calmon, Juan G. Restrepo, Joaquín J. Torres +1
Topological signals defined on nodes, links and higher dimensional simplices define the dynamical state of a network or of a simplicial complex. As such, topological signals are at…
Geometry, Topology and Simplicial Synchronization
Ana Paula Millán, Juan G. Restrepo, Joaquín J. Torres +1
Simplicial synchronization reveals the role that topology and geometry have in determining the dynamical properties of simplicial complexes. Simplicial network geometry and topolog…
Higher-order simplicial synchronization of coupled topological signals
Reza Ghorbanchian, Juan G. Restrepo, Joaquín J. Torres +1
Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fu…
Dynamic regulation of resource transport induces criticality in interdependent networks of excitable units
Yogesh S. Virkar, Juan G. Restrepo, Woodrow L. Shew +1
Various functions of a network of excitable units can be enhanced if the network is in the `critical regime', where excitations are, on average, neither damped nor amplified. An im…
Statistical Properties of Avalanches in Networks
Daniel B. Larremore, Marshall Y. Carpenter, Edward Ott +1
We characterize the distributions of size and duration of avalanches propagating in complex networks. By an avalanche we mean the sequence of events initiated by the externally sti…
A network-specific approach to percolation in networks with bidirectional links
Dane Taylor, Juan G. Restrepo
Methods for determining the percolation threshold usually study the behavior of network ensembles and are often restricted to a particular type of probabilistic node/link removal s…
Effects of network topology, transmission delays, and refractoriness on the response of coupled excitable systems to a stochastic stimulus
Daniel B. Larremore, Woodrow L. Shew, Edward Ott +1
We study the effects of network topology on the response of networks of coupled discrete excitable systems to an external stochastic stimulus. We extend recent results that charact…
Predicting criticality and dynamic range in complex networks: effects of topology
Daniel B. Larremore, Woodrow L. Shew, Juan G. Restrepo
The collective dynamics of a network of coupled excitable systems in response to an external stimulus depends on the topology of the connections in the network. Here we develop a g…
Approximating the largest eigenvalue of network adjacency matrices
Juan G. Restrepo, Edward Ott, Brian R. Hunt
The largest eigenvalue of the adjacency matrix of a network plays an important role in several network processes (e.g., synchronization of oscillators, percolation on directed netw…
Characterizing the dynamical importance of network nodes and links
J. G. Restrepo, E. Ott, B. R. Hunt
The largest eigenvalue of the adjacency matrix of the networks is a key quantity determining several important dynamical processes on complex networks. Based on this fact, we prese…
The emergence of coherence in complex networks of heterogeneous dynamical systems
Juan G. Restrepo, Edward Ott, Brian R. Hunt
We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the indi…
The onset of synchronization in large networks of coupled oscillators
Juan G. Restrepo, Brian R. Hunt, Edward Ott
We study the transition from incoherence to coherence in large networks of coupled phase oscillators. We present various approximations that describe the behavior of an appropriate…
Desynchronization waves and localized instabilities in oscillator arrays
Juan G. Restrepo, Edward Ott, Brian R. Hunt
We consider a ring of identical or near identical coupled periodic oscillators in which the connections have randomly heterogeneous strength. We use the master stability function m…