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Conserved dynamical systems are generally considered to be critical. We study a class of critical routing models, equivalent to random maps, which can be solved rigorously in the thermodynamic limit. The information flow is conserved for…
We explore the behaviour of chaotic oscillators in hierarchical networks coupled to an external chaotic system whose intrinsic dynamics is dissimilar to the other oscillators in the network. Specifically, each oscillator couples to the…
Recurrently coupled oscillators that are sufficiently heterogeneous and/or randomly coupled can show an asynchronous activity in which there are no significant correlations among the units of the network. The asynchronous state can…
Real world systems comprised of coupled oscillators have the ability to exhibit spontaneous synchronization and other complex behaviors. The interplay between the underlying network topology and the emergent dynamics remains a rich area of…
Frequency modulation by perturbation is the essential trait that differentiates limit cycle oscillators from phase oscillators. We studied networks of identical limit cycle oscillators whose frequencies are modulated sensitively by the…
A variety of physical, social and biological systems generate complex fluctuations with correlations across multiple time scales. In physiologic systems, these long-range correlations are altered with disease and aging. Such correlated…
We study the transition probability and coherence of a two-site system, interacting with an oscillator. Both properties depend on the initial preparation. The oscillator is prepared in a thermal state and, even though it cannot be…
A large variety of rhythms are observed in nature. Rhythms such as electroencephalogram signals in the brain can often be regarded as interacting. In this study, we investigate the dynamical properties of rhythmic systems in two populations…
We propose a network of oscillators to retrieve given patterns in which the oscillators keep a fixed phase relationship with one another. In this description, the phase and the amplitude of the oscillators can be regarded as the timing and…
In this tutorial, three examples of stochastic systems are considered: A strongly-damped oscillator, a weakly-damped oscillator and an undamped oscillator (integrator) driven by noise. The evolution of these systems is characterized by the…
Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…
In this work we analyze the solutions of a simple system of coupled phase oscillators in which the connectivity is learned dynamically. The model is inspired in the process of learning of birdsong by oscine birds. An oscillator acts as the…
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…
A foremost challenge in modern network science is the inverse problem of reconstruction (inference) of coupling equations and network topology from the measurements of the network dynamics. Of particular interest are the methods that can…
We investigate synchronization in complex networks of noisy phase oscillators. We find that, while too weak a coupling is not sufficient for the whole system to synchronize, too strong a coupling induces a nontrivial type of phase slip…
We explore the dynamical consequences of switching the coupling form in a system of coupled oscillators. We consider two types of switching, one where the coupling function changes periodically and one where it changes probabilistically. We…
An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the…
Power system coherency refers to the phenomenon that machines in a power network exhibit similar frequency responses after disturbances, and is foundational for model reduction and control design. Despite abundant empirical observations,…
Nonlinear complex network-coupled systems typically have multiple stable equilibrium states. Following perturbations or due to ambient noise, the system is pushed away from its initial equilibrium and, depending on the direction and the…
We explore oscillatory behaviour in a family of periodically driven spin chains which are subject to a weak measurement followed by post-selection. We discover a transition to an oscillatory phase as the strength of the measurement is…