Related papers: Interlayer antisynchronization in degree-biased du…
Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering,…
We present a global algorithm for training multilayer neural networks in this Letter. The algorithm is focused on controlling the local fields of neurons induced by the input of samples by random adaptations of the synaptic weights. Unlike…
We consider the problem of maximizing the synchronizability of oscillator networks by assigning weights and directions to the links of a given interaction topology. We first extend the well-known master stability formalism to the case of…
We develop a gradient-like algorithm to minimize a sum of peer objective functions based on coordination through a peer interconnection network. The coordination admits two stages: the first is to constitute a gradient, possibly with…
We study, numerically and analytically, the stability of synchronization for an ensemble of coupled phase oscillators with attractive and repulsive interactions, as a function of the number of repulsive couplings and their intensity.…
An outstanding problem in the study of networks of heterogeneous dynamical units concerns the development of rigorous methods to probe the stability of synchronous states when the differences between the units are not small. Here, we…
In-phase synchronization is a special case of synchronous behavior when coupled oscillators have the same phases for any time moments. Such behavior appears naturally for nearly identical coupled limit-cycle oscillators when the coupling…
Many real-world network are multilayer, with nontrivial correlations across layers. Here we show that these correlations amplify geometry in networks. We focus on mutual clustering--a measure of the amount of triangles that are present in…
In this paper, we study the simultaneous stability problem of a finite number of locally inter-connected linear subsystems under practical constraints, including asynchronous and aperiodic sampling, time-varying delays, and measurement…
To design control strategies that predictably manipulate a system's behavior, it is first necessary to understand how the system's structure relates to its response. Many complex systems can be represented as multilayer networks whose…
By a model of coupled phase oscillators, we show analytically how synchronization in {\em non-identical} complex networks can be enhanced by introducing a proper gradient into the couplings. It is found that, by pointing the gradient from…
In this manuscript, we study the problem of robust synchronization in networks of diffusively time-delayed coupled nonlinear systems. In particular, we prove that, under some mild conditions on the input-output dynamics of the systems and…
The interactions among the elementary components of many complex systems can be qualitatively different. Such systems are therefore naturally described in terms of multiplex or multi-layer networks, i.e. networks where each layer stands for…
This work considers the timescales associated with the global order parameter and the interlayer synchronization of coupled Kuramoto oscillators on multiplexes. For the two-layer multiplexes with initially high degree of synchronization in…
The multiplex network growth literature has been confined to homogeneous growth hitherto, where the number of links that each new incoming node establishes is the same across layers. This paper focuses on heterogeneous growth. We first…
Adaptive networks change their connectivity with time, depending on their dynamical state. While synchronization in structurally static networks has been studied extensively, this problem is much more challenging for adaptive networks. In…
We present the emergence of chimeras, a state referring to coexistence of partly coherent, partly incoherent dynamics in networks of identical oscillators, in a multiplex network consisting of two non-identical layers which are…
Understanding the inductive bias and generalization properties of large overparametrized machine learning models requires to characterize the dynamics of the training algorithm. We study the learning dynamics of large two-layer neural…
Tunneling and Coulomb drag are sensitive probes of spontaneous interlayer phase coherence in bilayer two-dimensional electron systems at total Landau level filling factor $\nu_T = 1$. We find that the phase boundary between the interlayer…
This study investigates the suitability of the annealed approximation in high-dimensional systems characterized by dense networks with quenched link disorder, employing models of coupled oscillators. We demonstrate that dynamic equations…