542 citations · 2.9k across the 29 of their papers we have counts for
15 papers · 1 filter
Early warning signals for phase transitions in networks
A. V. Goltsev, S. N. Dorogovtsev
The percolation phase transition in complex network systems attracts much attention and has numerous applications in various research fields. Finite size effects smooth the transit…
Structural stability of interaction networks against negative external fields
S. Yoon, A. V. Goltsev, J. F. F. Mendes
We explore structural stability of weighted and unweighted networks of positively interacting agents against a negative external field. We study how the agents support the activity…
Sensitivity of directed networks to the addition and pruning of edges and vertices
A. V. Goltsev, G. Timár, J. F. F. Mendes
We study the sensitivity of directed complex networks to the addition and pruning of edges and vertices and introduce the susceptibility, which quantifies this sensitivity. We show…
A unified approach to percolation processes on multiplex networks
G. J. Baxter, D. Cellai, S. N. Dorogovtsev +2
Many real complex systems cannot be represented by a single network, but due to multiple sub-systems and types of interactions, must be represented as a multiplex network. This is…
Mapping the Structure of Directed Networks: Beyond the "Bow-tie" Diagram
G. Timár, A. V. Goltsev, S. N. Dorogovtsev +1
We reveal a hierarchical, multilayer organization of finite components -- i.e., tendrils and tubes -- around the giant connected components in directed networks and propose efficie…
Synchronization in the random field Kuramoto model on complex networks
M. A. Lopes, E. M. Lopes, S. Yoon +2
We study the impact of random pinning fields on the emergence of synchrony in the Kuramoto model on complete graphs and uncorrelated random complex networks. We consider random fie…
Critical dynamics of the k-core pruning process
G. J. Baxter, S. N. Dorogovtsev, K. -E. Lee +2
We present the theory of the k-core pruning process (progressive removal of nodes with degree less than k) in uncorrelated random networks. We derive exact equations describing thi…
Solution of the explosive percolation quest. II. Infinite-order transition produced by the initial distributions of clusters
R. A. da Costa, S. N. Dorogovtsev, A. V. Goltsev +1
We describe the effect of power-law initial distributions of clusters on ordinary percolation and its generalizations, specifically, models of explosive percolation processes based…
Solution of the explosive percolation quest: Scaling functions and critical exponents
R. A. da Costa, S. N. Dorogovtsev, A. V. Goltsev +1
Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase…
Critical exponents of the explosive percolation transition
R. A. da Costa, S. N. Dorogovtsev, A. V. Goltsev +1
In a new type of percolation phase transition, which was observed in a set of non-equilibrium models, each new connection between vertices is chosen from a number of possibilities…
Kuramoto model with frequency-degree correlations on complex networks
B. C. Coutinho, A. V. Goltsev, S. N. Dorogovtsev +1
We study the Kuramoto model on complex networks, in which natural frequencies of phase oscillators and the vertex degrees are correlated. Using the annealed network approximation a…
Neural networks with dynamical synapses: from mixed-mode oscillations and spindles to chaos
K. -E. Lee, A. V. Goltsev, M. A. Lopes +1
Understanding of short-term synaptic depression (STSD) and other forms of synaptic plasticity is a topical problem in neuroscience. Here we study the role of STSD in the formation…
Critical and resonance phenomena in neural networks
A. V. Goltsev, M. A. Lopes, K. -E. Lee +1
Brain rhythms contribute to every aspect of brain function. Here, we study critical and resonance phenomena that precede the emergence of brain rhythms. Using an analytical approac…
"Explosive Percolation" Transition is Actually Continuous
R. A. da Costa, S. N. Dorogovtsev, A. V. Goltsev +1
The basic notion of percolation in physics assumes the emergence of a giant connected (percolation) cluster in a large disordered system when the density of connections exceeds som…
Stochastic cellular automata model of neural networks
A. V. Goltsev, F. V. de Abreu, S. N. Dorogovtsev +1
We propose a stochastic dynamical model of noisy neural networks with complex architectures and discuss activation of neural networks by a stimulus, pacemakers and spontaneous acti…