Related papers: Phase transition in a class of non-linear random n…
We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be…
What is the reason for complex dynamical patterns registered from real biological neuronal networks? Noise and dynamical reconfiguring of a network (functional/dynamic connectome) were proposed as possible answers. In this case study, we…
We suggest a model for data losses in a single node of a packet-switched network (like the Internet) which reduces to one-dimensional discrete random walks with unusual boundary conditions. The model shows critical behavior with an abrupt…
Multiple dynamic pathways always exist in biological networks, but their robustness against internal fluctuations and relative stability have not been well recognized and carefully analyzed yet. Here we try to address these issues through…
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 approach and simulations of a cortical circuit model of neural…
Dynamic systems characterized by diversified evolutions are not only more flexible, but also more resilient to attacks, failures and changing conditions. This article addresses the quantification of the diversity of non-linear transient…
The focus of this thesis is about statistical mechanics on heterogeneous random graphs, i.e. how this heterogeneity affects the cooperative behavior of model systems. It is not intended as a review on it, rather it is showed how this…
The critical Kauffman model with connectivity one is the simplest class of critical Boolean networks. Nevertheless, it exhibits intricate behavior at the boundary of order and chaos. We introduce a formalism for expressing the dynamics of…
Adaptive network is a powerful presentation to describe different real-world phenomena. However, current models often neglect higher-order interactions (beyond pairwise interactions) and diverse adaptation types (cooperative and…
Consider a graph where each of the $n$ nodes is either in state $\mathcal{R}$ or $\mathcal{B}$. Herein, we analyze the \emph{synchronous $k$-Majority dynamics}, where in each discrete-time round nodes simultaneously sample $k$ neighbors…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
A certain complexity threshold is proposed which defines the term `complex network' for RSN, e.g. Kauffman networks with s>=2 - more than two equally probable state variants. Such Kauffman networks are no longer Boolean networks. RSN are…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with…
Understanding how deep neural networks learn remains a fundamental challenge in modern machine learning. A growing body of evidence suggests that training dynamics undergo a distinct phase transition, yet our understanding of this…
Critical learning periods are periods early in development where temporary sensory deficits can have a permanent effect on behavior and learned representations. Despite the radical differences between biological and artificial networks,…
Continuous-time systems with switch-like behaviour occur in chemical kinetics, gene regulatory networks and neural networks. Networks with hard switching, as a limiting case of smooth sigmoidal switching, retain the richest possible range…
The self-consistent probabilistic approach has proven itself powerful in studying the percolation behavior of interdependent or multiplex networks without tracking the percolation process through each cascading step. In order to understand…
We use a recently proposed class of tensor-network states to study phase transitions in string-net models. These states encode the genuine features of the string-net condensate such as, e.g., a nontrivial perimeter law for Wilson loops…
We investigate the network model of community by Watts, Dodds and Newman (D. J. Watts et al., Science 296 (2002) 1302) as a hierarchy of groups, each of 5 individuals. A homophily parameter $\alpha$ controls the probability proportional to…