Related papers: Delayed Dynamical Systems: Networks, Chimeras and …
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…
Recently we demonstrated experimentally that microwave oscillators based on the time delay feedback provided by traveling spin waves could operate as reservoir computers. In the present paper, we extend this concept by adding the feature of…
Forecasting the dynamics of large complex networks from previous time-series data is important in a wide range of contexts. Here we present a machine learning scheme for this task using a parallel architecture that mimics the topology of…
Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial…
Reverse engineering of complex dynamical networks is important for a variety of fields where uncovering the full topology of unknown networks and estimating parameters characterizing the network structure and dynamical processes are of…
Anticipated synchronisation occurs when a driven dynamical system synchronises with the future state of the driver system to which it is unidirectionally coupled. Previous theoretical and experimental studies have focused on setups with a…
Patterned nanomagnet arrays (PNAs) have been shown to exhibit a strong geometrically frustrated dipole interaction. Some PNAs have also shown emergent domain wall dynamics. Previous works have demonstrated methods to physically probe these…
We investigated interactions within chimera states in a phase oscillator network with two coupled subpopulations. To quantify interactions within and between these subpopulations, we estimated the corresponding (delayed) mutual information…
The chimera state with co-existing coherent-incoherent dynamics has recently attracted a lot of attention due to its wide applicability. We investigate non-locally coupled identical chaotic maps with delayed interactions in the multiplex…
Delayed interactions are a common property of coupled natural systems and therefore arise in a variety of different applications. For instance, signals in neural or laser networks propagate at finite speed giving rise to delayed…
We consider a network of delay dynamical systems connected in a ring via unidirectional positive feedback with constant delay in coupling. For the specific case of Mackey-Glass systems on the ring topology, we capture the phenomena of…
This study investigates the impact of delayed coupling on the global and local synchronization of identical coupled oscillators residing in a ring. Utilizing the Kuramoto model, we examine the effects of delayed coupling on collective…
Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…
Physical reservoir computing is a computational framework that offers an energy- and computation-efficient alternative to conventional training of neural networks. In reservoir computing, input signals are mapped into the high-dimensional…
In this manuscript, we study the problem of robust synchronization in networks of diffusively time-delayed coupled nonlinear systems. In particular, we prove that, under some mild conditions on the input-output dynamics of the systems and…
A theory of time-delayed coherent quantum feedback is developed. More specifically, we consider a quantum system coupled to a bosonic reservoir creating a unidirectional feedback loop. It is shown that the dynamics can be mapped onto a…
This study examines the complex interplay between inertia and time delay in regular rotor networks within the framework of the second-order Kuramoto model. By combining analytical and numerical methods, we demonstrate that intrinsic time…
Dynamical networks with time delays can pose a considerable challenge for mathematical analysis. Here, we extend the approach of generalized modeling to investigate the stability of large networks of delay-coupled delay oscillators. When…
The Deep Time-Delay Reservoir Computing concept utilizes unidirectionally connected systems with time-delays for supervised learning. We present how the dynamical properties of a deep Ikeda-based reservoir are related to its memory capacity…
A new machine learning scheme, termed versatile reservoir computing, is proposed for sustaining the dynamics of heterogeneous complex networks. We show that a single, small-scale reservoir computer trained on time series from a subset of…