Related papers: Contraction and Synchronization in Reservoir Syste…
A minimal model for reservoir computing is studied. We demonstrate that a reservoir computer exists that emulates given coupled maps by constructing a modularized network. We describe a possible mechanism for collapses of the emulation in…
We study the problem of synchronizing a general complex network by means of an adaptive strategy in the case where the network topology is slowly time varying and every node receives at each time only one aggregate signal from the set of…
In this paper a novel discrete-time realization of the super-twisting controller is proposed. The closed-loop system is proven to converge to an invariant set around the origin in finite time. Furthermore, the steady-state error is shown to…
This paper introduces a novel approach to predicting periodic time series using reservoir computing. The model is tailored to deliver precise forecasts of rhythms, a crucial aspect for tasks such as generating musical rhythm. Leveraging…
We propose, analyze, and test a novel continuous data assimilation two-phase flow algorithm for reservoir simulation. We show that the solutions of the algorithm, constructed using coarse mesh observations, converge at an exponential rate…
We derive the fluctuation theorem for a stochastic and periodically driven system coupled to two reservoirs with the aid of a master equation. We write down the cumulant generating functions for both the current and entropy production in…
We study synchronisation properties of networks of coupled dynamical systems with interaction akin to diffusion. We assume that the isolated node dynamics possesses a forward invariant set on which it has a bounded Jacobian, then we…
Synchronisation and pattern formation have been intensely addressed for systems evolving on static networks. Extending the study to include the inherent ability of the network to adjust over time proved cumbersome and led to conclusions…
This paper addresses the problem of giving conditions for transcriptional systems to be globally entrained to external periodic inputs. By using contraction theory, a powerful tool from dynamical systems theory, it is shown that certain…
Reservoir computers (RC) have proven useful as surrogate models in forecasting and replicating systems of chaotic dynamics. The quality of surrogate models based on RCs is crucially dependent on their optimal implementation that involves…
We study the synchronization behavior of discrete-time Markov chains on countable state spaces. Representing a Markov chain in terms of a random dynamical system, which describes the collective dynamics of trajectories driven by the same…
Concurrent synchronization is a regime where diverse groups of fully synchronized dynamic systems stably coexist. We study global exponential synchronization and concurrent synchronization in the context of Lagrangian systems control. In a…
Reservoir computing systems, a class of recurrent neural networks, have recently been exploited for model-free, data-based prediction of the state evolution of a variety of chaotic dynamical systems. The prediction horizon demonstrated has…
Stability of synchronization in delay-coupled networks of identical units generally depends in a complicated way on the coupling topology. We show that for large coupling delays synchronizability relates in a simple way to the spectral…
The synchronization of coupled chaotic systems represents a fundamental example of self organization and collective behavior. This well-studied phenomenon is classically characterized in terms of macroscopic parameters, such as Lyapunov…
Time delays increase the effective dimensionality of reservoirs, thus suggesting that time delays in reservoirs can enhance their performance, particularly their memory and prediction abilities. We find new closed-form expressions for…
Reservoir computing can embed attractors into random neural networks (RNNs), generating a ``mirror'' of a target attractor because of its inherent symmetrical constraints. In these RNNs, we report that an attractor-merging crisis…
We explore the hyperparameter space of reservoir computers used for forecasting of the chaotic Lorenz '63 attractor with Bayesian optimization. We use a new measure of reservoir performance, designed to emphasize learning the global climate…
We construct compositional continuous approximations for an interconnection of infinitely many discrete-time switched systems. An approximation (known as abstraction) is itself a continuous-space system, which can be used as a replacement…
We show that global generalized synchronization (GS) exists in structurally different time-delay systems, even with different orders, with quite different fractal (Kaplan-Yorke) dimensions, which emerges via partial GS in symmetrically…