Related papers: Learning the dynamics of coupled oscillators from …

Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…

In nonlinear dynamical systems, tipping refers to a critical transition from one steady state to another, typically catastrophic, steady state, often resulting from a saddle-node bifurcation. Recently, the machine-learning framework of…

We study the dynamics of coupled oscillator networks with higher-order interactions and their ability to store information. In particular, the fixed points of these oscillator systems consist of two clusters of oscillators that become…

In this paper we review recent work on novel computing paradigms using coupled oscillatory dynamical systems. We explore systems of relaxation oscillators based on linear state transitioning devices, which switch between two discrete states…

Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…

We present a novel, model-free, and data-driven methodology for controlling complex dynamical systems into previously unseen target states, including those with significantly different and complex dynamics. Leveraging a parameter-aware…

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…

The dynamical behaviour of many-body systems is often richer than what can be anticipated from their static properties. Here we show that in closed quantum systems this becomes evident by considering time-integrated observables as order…

Reservoir computing has been shown to be a useful framework for predicting critical transitions of a dynamical system if the bifurcation parameter is also provided as an input. Its utility is significant because in real-world scenarios, the…

We establish the potential of continuous-variable Gaussian states of linear dynamical systems for machine learning tasks. Specifically, we consider reservoir computing, an efficient framework for online time series processing. As a…

Model-free and data-driven prediction of tipping point transitions in nonlinear dynamical systems is a challenging and outstanding task in complex systems science. We propose a novel, fully data-driven machine learning algorithm based on…

Open quantum many-body systems with controllable dissipation can exhibit novel features in their dynamics and steady states. A paradigmatic example is the dissipative transverse field Ising model. It has been shown recently that the steady…

The dynamics of open quantum systems connected with several reservoirs attract great attention due to its importance in quantum optics, biology, quantum thermodynamics, transport phenomena, etc. In many problems, the Born approximation is…

We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor, but in its vicinity as well. For this we consider systems perturbed by an external force. This allows us to not merely…

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…

We demonstrate a data-driven technique for adaptive control in dynamical systems that exploits the reservoir computing method. We show that a reservoir computer can be trained to predict a system parameter from the time series data.…

This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…

We investigate the transient dynamics of the quantum Stuart-Landau oscillator, a paradigmatic quantum system exhibiting a quantum limit cycle and synchronization. From the energy dynamics, we determine a condition for the classical regime…

In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions…

There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…