Related papers: Detection of Generalized Synchronization using Ech…
As an efficient recurrent neural network (RNN) model, reservoir computing (RC) models, such as Echo State Networks, have attracted widespread attention in the last decade. However, while they have had great success with time series data…
We demonstrate the existence of generalized synchronization in systems that act as mediators between two dynamical units that, in turn, show complete synchronization with each other. These are the so-called relay systems. Specifically, we…
We explore the interplay of network structure, topology, and dynamic interactions between nodes using the paradigm of distributed synchronization in a network of coupled oscillators. As the network evolves to a global steady state,…
We present an approach which enables to identify phase synchronization in coupled chaotic oscillators without having to explicitly measure the phase. We show that if one defines a typical event in one oscillator and then observes another…
Echo-state networks are simple models of discrete dynamical systems driven by a time series. By selecting network parameters such that the dynamics of the network is contractive, characterized by a negative maximal Lyapunov exponent, the…
We propose an innovative design for an optical Echo State Network (ESN), an advanced type of reservoir computer known for its universal computational capabilities. Our design enables an optical implementation of arbitrary ESNs, featuring…
A new method for secure information transmission based on generalized synchronization is proposed. The principal advantage of it is a remarkable stability to noise. To reveal this peculiarity of the proposed method the effectiveness of the…
Echo State Networks (ESNs) are a particular type of untrained Recurrent Neural Networks (RNNs) within the Reservoir Computing (RC) framework, popular for their fast and efficient learning. However, traditional ESNs often struggle with…
Echo State Networks (ESNs) are a class of single layer recurrent neural networks that have enjoyed recent attention. In this paper we prove that a suitable ESN, trained on a series of measurements of an invertible dynamical system, induces…
We characterize synchronization phenomenon in discrete-time, discrete-state random dynamical systems, with random and probabilistic Boolean networks as particular examples. In terms of multiplicative ergodic properties of the induced linear…
Echo State Networks (ESNs) are typically presented as efficient, readout-trained recurrent models, yet their dynamics and design are often guided by heuristics rather than first principles. We recast ESNs explicitly as state-space models…
The goal of this paper is to investigate the theoretical properties, the training algorithm, and the predictive control applications of Echo State Networks (ESNs), a particular kind of Recurrent Neural Networks. First, a condition…
It is a widely accepted fact that data representations intervene noticeably in machine learning tools. The more they are well defined the better the performance results are. Feature extraction-based methods such as autoencoders are…
Data are often sampled irregularly in time. Dealing with this using Recurrent Neural Networks (RNNs) traditionally involved ignoring the fact, feeding the time differences as additional inputs, or resampling the data. All these methods have…
This paper deals with the chaotic oscillator synchronization. A new approach to detect the synchronized behaviour of chaotic oscillators has been proposed. This approach is based on the analysis of different time scales in the time series…
Long-lead forecasting for spatio-temporal systems can often entail complex nonlinear dynamics that are difficult to specify it a priori. Current statistical methodologies for modeling these processes are often highly parameterized and thus,…
We report on partial and global generalized synchronization in exemplar bidirectionally coupled non-identical chaotic systems with multiple time delays. We derive conditions for such synchronization regimes. The general approach is applied…
In this paper, we investigate the development of generalized synchronization (GS) on typical complex networks, such as scale-free networks, small-world networks, random networks and modular networks. By adopting the auxiliary-system…
A basic result in synchronization of linear systems via output coupling is presented. For identical discrete-time linear systems that are detectable from their outputs and neutrally stable, it is shown that a linear output feedback law…
Temporal data modelling techniques with neural networks are useful in many domain applications, including time-series forecasting and control engineering. This paper aims at developing a recurrent version of stochastic configuration…