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It is well known that the addition of noise to a multistable dynamical system can induce random transitions from one stable state to another. For low noise, the times between transitions have an exponential tail and Kramers' formula gives…
Synchronization is an omnipresent collective phenomenon in nature and technology, whose understanding is in particular for real-world systems still elusive. We study the synchronization transition in a phase oscillator system with two…
We report on finite-sized-induced transitions to synchrony in a population of phase oscillators coupled via a nonlinear mean field, which microscopically is equivalent to a hypernetwork organization of interactions. Using a self-consistent…
We study synchronization of sinusoidally coupled phase oscillators on networks with modular structure and a large number of oscillators in each community. Of particular interest is the hierarchy of local and global synchrony, i.e.,…
We consider a population of globally coupled oscillators driven by common noise. By applying the Ott-Antonsen ansatz and by averaging over the fast oscillations, we obtain analytically tractable equations for the noisy evolution of the…
Intermittent synchronization is observed in a variety of different experimental settings in physics and beyond and is an established research topic in nonlinear dynamics. When coupled oscillators exhibit relatively weak, intermittent…
Weakly coupled limit cycle oscillators can be reduced into a system of weakly coupled phase models. These phase models are helpful to analyze the synchronization phenomena. For example, a phase model of two oscillators has a one-dimensional…
A theoretical analysis is presented to show the general occurrence of phase clusters in weakly, globally coupled oscillators close to a Hopf bifurcation. Through a reductive perturbation method, we derive the amplitude equation with a…
We design, characterize, and couple Boolean phase oscillators that include state-dependent feedback delay. The state-dependent delay allows us to realize an adjustable coupling strength, even though only Boolean signals are exchanged.…
Motivated from a wide range of applications, various methods to control synchronization in coupled oscillators have been proposed. Previous studies have demonstrated that global feedback typically induces three macroscopic behaviors:…
The ubiquitous occurrence of cluster patterns in nature still lacks a comprehensive understanding. It is known that the dynamics of many such natural systems is captured by ensembles of Stuart-Landau oscillators. Here, we investigate…
We experimentally demonstrate group synchrony in a network of four nonlinear optoelectronic oscillators with time-delayed coupling. We divide the nodes into two groups of two each, by giving each group different parameters and by enabling…
We considered the phase coherence dynamics in a Two-Frequency and Two-Coupling (TFTC) model of coupled oscillators, where coupling strength and natural oscillator frequencies for individual oscillators may assume one of two values…
We study the synchronization of a linear array of globally coupled identical logistic maps. We consider a time-delayed coupling that takes into account the finite velocity of propagation of the interactions. We find globally synchronized…
We generalize the Kuramoto model of coupled oscillators to allow time-delayed interactions. New phenomena include bistability between synchronized and incoherent states, and unsteady solutions with time-dependent order parameters. We derive…
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…
We report the nature of transitions from nonsynchronous to complete synchronization (CS) state in arrays of time-delay systems, where the systems are coupled with instantaneous diffusive coupling. We demonstrate that the transition to CS…
Synchronization processes play critical roles in the functionality of a wide range of both natural and man-made systems. Recent work in physics and neuroscience highlights the importance of higher-order interactions between dynamical units,…
A system's response to external periodic changes can provide crucial information about its dynamical properties. We investigate the synchronization transition, an archetypical example of a dynamic phase transition, in the framework of such…
Networks of interacting nodes connected by edges arise in almost every branch of scientific enquiry. The connectivity structure of the network can force the existence of invariant subspaces, which would not arise in generic dynamical…