Related papers: Synchronization in random balanced networks
Synchronization and resonance on networks are some of the most remarkable collective dynamical phenomena. The network topology, or the nature and distribution of the connections within an ensemble of coupled oscillators, plays a crucial…
Percolation and synchronization are two phase transitions that have been extensively studied since already long ago. A classic result is that, in the vast majority of cases, these transitions are of the second-order type, i.e. continuous…
The problem of synchronization in heterogeneous networks of linear systems with nonlinear delayed diffusive coupling is considered. The network is presented in new coordinates mean-field dynamics and synchronization errors. Thus the problem…
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 individual uncoupled systems to be either chaotic or periodic,…
We study the transition to synchronization in large, dense networks of chaotic circle maps, where an exact solution of the mean-field dynamics in the infinite network and all-to-all coupling limit is known. In dense networks of finite size…
Networks of strongly-coupled neurons with random connectivity exhibit chaotic, asynchronous fluctuations. In previous work, we showed that when endowed with an additional low-rank connectivity consisting of the outer product of orthogonal…
In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We…
This article investigates the emergence of phase synchronization in a network of randomly connected neurons by chemical synapses. The study uses the classic Hodgkin-Huxley model to simulate the neuronal dynamics under the action of a train…
Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns…
The study of balanced networks of excitatory and inhibitory neurons has led to several open questions. On the one hand it is yet unclear whether the asynchronous state observed in the brain is autonomously generated, or if it results from…
The "edge of chaos" phase transition in artificial neural networks is of renewed interest in light of recent evidence for criticality in brain dynamics. Statistical mechanics traditionally studied this transition with connectivity $k$ as…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
We describe the dynamics of a simple adaptive network. The network architecture evolves to a number of disconnected components on which the dynamics is characterized by the possibility of differently synchronized nodes within the same…
Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is…
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…
Endowing brain anatomy, dynamics, and function with a network structure is becoming standard in neuroscience. In its simplest form, a network is a collection of units and relationships between them. The pattern of relations among the units…
Networks in nature do not act in isolation but instead exchange information, and depend on each other to function properly. An incipient theory of Networks of Networks have shown that connected random networks may very easily result in…
The behavior of the network and its stability are governed by both dynamics of individual nodes as well as their topological interconnections. Attention mechanism as an integral part of neural network models was initially designed for…
We investigate the emergence of synchronization in a network of coupled chaotic macroeconomic systems. Each node represents an economy characterized by three key variables savings, gross domestic product (GDP), and foreign capital inflows.…
Network coherence generally refers to the emergence of simple aggregated dynamical behaviours, despite heterogeneity in the dynamics of the subsystems that constitute the network. In this paper, we develop a general frequency domain…