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Quenched or frozen-in structural disorder is ubiquitous in real experimental systems. Much of the progress is achieved in understanding the phase separation of such systems using the diffusion-driven coarsening in Ising model with quenched…

The center of mass motion of trapped ions and neutral atoms is suitable for approximation by a time-dependent driven quantum harmonic oscillator whose frequency and driving strength may be controlled with high precision. We show the time…

Diverse complex systems often undergo sudden changes in their states, such as epileptic seizures, climate changes, and social uprisings. Such behavior has been modeled by noise-induced escape of bistable elements, which is the escape from…

We explore the behaviour of an ensemble of chaotic oscillators coupled only to an external chaotic system, whose intrinsic dynamics may be similar or dissimilar to the group. Counter-intuitively, we find that a dissimilar external system…

Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…

Fluid flows play a central role in scientific and technological development, and many of these flows are characterized by a dominant oscillation, such as the vortex shedding in the wake of nearly all transportation vehicles. The ability to…

In this paper we present a comprehensive analysis of the coherence phenomenon of two coupled dissipative oscillators. The action of a classical driving field on one of the oscillators is also analyzed. Master equations are derived for both…

Periodic forcing of nonlinear oscillators generates a rich and complex variety of behaviors, ranging from regular to chaotic behavior. In this work we seek to control, i.e., either suppress or generate, the chaotic behavior of a classical…

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…

When an isolated quantum system is driven out of equilibrium, expectation values of general observables start oscillating in time. This article reviews the general theory of such temporal fluctuations. We first survey some results on the…

Self-oscillations underlie many natural phenomena such as heartbeat, ocean waves, and the pulsation of variable stars. From pendulum clocks to the behavior of animal groups, self-oscillation is one of the keys to the understanding of…

We investigate the weak-strong coupling transition of two linearly coupled systems under the influence of a phase fluctuating coupling. In the weak coupling regime the exponential decay of quantum properties is well known. A different…

We develop Bayesian state space methods for modelling changes to the mean level or temporal correlation structure of an observed time series due to intermittent coupling with an unobserved process. Novel intervention methods are proposed to…

An ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses shows a range of non-trivial behavior, from synchronization, desynchronization, to clustering. The group behavior that arises in the ensemble can be…

We present a simple theory accounting for two central observations in a recent experiment on quantum coarsening and collective dynamics on a programmable quantum simulator [T. Manovitz et al., Nature \textbf{638}, 86 (2025)]: an apparent…

We explore analytically the oscillation quenching phenomena (amplitude death and oscillation death) in a coupled third order phase locked loop (PLL) both in periodic and chaotic mode. The phase locked loops are coupled through mean field…

We consider a mean-field model of coupled phase oscillators with quenched disorder in the coupling strengths and natural frequencies. When these two kinds of disorder are uncorrelated (and when the positive and negative couplings are equal…

Whereas the importance of transient dynamics to the functionality and management of complex systems has been increasingly recognized, most of the studies are based on models. Yet in realistic situations the models are often unknown and what…

We study the thermodynamic properties of a microscopic model of coupled oscillators that exhibits a dynamical phase transition from a desynchronized to a synchronized phase. We consider two different configurations for the thermodynamic…

Fluctuations and noise may alter the behavior of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We…