Related papers: Validity of annealed approximation in a high-dimen…
This paper investigates synchronization phenomena in networks of coupled oscillators governed by three-time-scale dynamical systems exhibiting canard dynamics. A mathematical framework has been developed to analyze the synchronization of…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…
Infinite projected entangled pair states (iPEPS), the tensor network ansatz for two-dimensional systems in the thermodynamic limit, already provide excellent results on ground-state quantities using either imaginary-time evolution or…
Oscillator networks found in social and biological systems are characterized by the presence of wide ranges of coupling strengths and complex organization. Yet robustness and synchronization of oscillations are found to emerge on…
We present high-accuracy quasi-stationary (QS) simulations of the contact process in quenched networks, built using the configuration model with both structural and natural cutoffs. The critical behavior is analyzed in the framework of the…
We study the effects of uniform time delays on the extreme fluctuations in stochastic synchronization and coordination problems with linear couplings in complex networks. We obtain the average size of the fluctuations at the nodes from the…
In these notes we study synchronizability of dynamical processes defined on complex networks as well as its interplay with network topology. Building from a recent work by Barahona and Pecora [Phys. Rev. Lett. 89, 054101 (2002)], we use a…
We investigate how free probability allows us to approximate the density of states in tight binding models of disordered electronic systems. Extending our previous studies of the Anderson model in neighbor interactions [J. Chen et al.,…
Does the assignment order of a fixed collection of slightly distinct subsystems into given communication channels influence the overall ensemble behavior? We discuss this question in the context of complex networks of non-identical…
The article considers systems of interacting particles on networks with adaptively coupled dynamics. Such processes appear frequently in natural processes and applications. Relying on the notion of graph convergence, we prove that for large…
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…
In a recent work, mean-field analysis and computer simulations were employed to analyze critical self-organization in networks of excitable cellular automata where randomly chosen synapses in the network were depressed after each spike (the…
Random Threshold Networks with sparse, asymmetric connections show complex dynamical behavior similar to Random Boolean Networks, with a transition from ordered to chaotic dynamics at a critical average connectivity $K_c$. In this type of…
Many mathematical models of interacting agents assume that individual interactions scale down in proportion to the network size, ensuring that the combined input received from the network does not diverge. In theoretical neuroscience,…
We study the asymptotic behaviour of a finite network of oscillators (harmonic or anharmonic) coupled to a number of deterministic Lagrangian thermostats of finite energy. In particular, we consider a chain of oscillators interacting with…
Networks of limit cycle oscillators can show intricate patterns of synchronization such as splay states and cluster synchronization. Here we analyze dynamical states that display a continuum of seemingly independent splay clusters. Each…
We analyze the synchronization transition for a pair of coupled identical Kauffman networks in the chaotic phase. The annealed model for Kauffman networks shows that synchronization appears through a transcritical bifurcation, and provides…
We address a distributed adaptive control methodology for nonlinear interconnected systems possibly affected by network anomalies. In the framework of adaptive approximation, the distributed controller and parameter estimator are designed…
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although…
We show that incompressible polar active fluids can exhibit an ordered, coherently moving phase even in the presence of quenched disorder in two dimensions. Unlike such active fluids with annealed (i.e., time-dependent) disorder only, which…