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Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between qualitatively distinct trajectories in a…
Polymerization of microtubules is ubiquitous in biological cells and under certain conditions it becomes oscillatory in time. Here simple reaction models are analyzed that capture such oscillations as well as the length distribution of…
Onset and loss of synchronization in coupled oscillators are of fundamental importance in understanding emergent behavior in natural and man-made systems, which range from neural networks to power grids. We report on experiments with…
We consider a neural field model which consists of a network of an arbitrary number of Wilson-Cowan nodes with homeostatic adjustment of the inhibitory coupling strength and time delayed, excitatory coupling. We extend previous work on this…
The emergence of rich dynamical phenomena in coupled self-sustained oscillators, primarily synchronization and amplitude death, has attracted considerable interest in several fields of science and engineering. Here, we present a…
We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of a small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is…
We study synchronization in populations of phase-coupled stochastic three-state oscillators characterized by a distribution of transition rates. We present results on an exactly solvable dimer as well as a systematic characterization of…
A density oscillator is a fluid system in which oscillatory flow occurs between different density fluids through the pore connecting them. We investigate the synchronization in coupled density oscillators using two-dimensional hydrodynamic…
We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with…
Experimental observations of typical kinds of synchronization transitions are reported in unidirectionally coupled time-delay electronic circuits with a threshold nonlinearity and two time delays, namely feedback delay $\tau_1$ and coupling…
The Kuramoto model provides a prototypical framework to synchronization phenomena in interacting particle systems. Apart from full phase synchrony where all oscillators behave identically, identical Kuramoto oscillators with ring-like…
Biologists have long observed periodic-like oxygen consumption oscillations in yeast populations under certain conditions and several unsatisfactory explanations for this phenomenon have been proposed. These "autonomous oscillations" have…
Networks of neural mass nodes with delayed interactions are increasingly being used as models for large-scale brain activity. To complement the growing number of computational studies of such networks, it is timely to develop new…
Network interactions between dynamical units are often subject to time delay. We develop a phase reduction method for delay-coupled oscillator networks. The method is based on rewriting the delay-differential equation as an ordinary…
Localized phenomena abound in nature and throughout the physical sciences. Some universal mechanisms for localization have been characterized, such as in the snaking bifurcations of localized steady states in pattern-forming partial…
We consider the inertial Kuramoto model of $N$ globally coupled oscillators characterized by both their phase and angular velocity, in which there is a time delay in the interaction between the oscillators. Besides the academic interest, we…
A novel regime of synchronization, called remote synchronization, where the peripheral nodes form a phase synchronized cluster not including the hub, was recently observed in star motifs. We show the existence of a more general dynamical…
By characterizing the phase dynamics in coupled oscillators, we gain insights into the fundamental phenomena of complex systems. The collective dynamics in oscillatory systems are often described by order parameters, which are insufficient…
We study systems of coupled units in a general network configuration with a coupling delay. We show that the destabilizing bifurcations from an equilibrium are governed by the extreme eigenvalues of the coupling matrix of the network. Based…
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…