Related papers: Dynamical analysis of a parameter-aware reservoir …

Reservoir computing - information processing based on untrained recurrent neural networks with random connections - is expected to depend on the nonlinear properties of the neurons and the resulting oscillatory, chaotic, or fixpoint…

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…

In applications of dynamical systems, situations can arise where it is desired to predict the onset of synchronization as it can lead to characteristic and significant changes in the system performance and behaviors, for better or worse. In…

Varying one of the governing parameters of a dynamical system may lead to a critical transition, where the new stable state is undesirable. In some cases, there is only a limited range of the bifurcation parameter that corresponds to that…

Reservoir computing derived from recurrent neural networks is more applicable to real world systems than deep learning because of its low computational cost and potential for physical implementation. Specifically, physical reservoir…

Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the…

Reservoir computing has proven effective for tasks such as time-series prediction, particularly in the context of chaotic systems. However, conventional reservoir computing frameworks often face challenges in achieving high prediction…

Transformer architectures have recently surged as promising solutions for nonlinear dynamical systems, proposed as foundation models capable of zero-shot dynamics reconstruction and forecasting. Despite this success, it remains unclear…

Reservoir computing (RC) offers efficient temporal data processing with a low training cost by separating recurrent neural networks into a fixed network with recurrent connections and a trainable linear network. The quality of the fixed…

Reconstructing the KAM dynamics diagram of Hamiltonian system from the time series of a limited number of parameters is an outstanding question in nonlinear science, especially when the Hamiltonian governing the system dynamics are unknown.…

Clean images are an important requirement for machine vision systems to recognize visual features correctly. However, the environment, optics, electronics of the physical imaging systems can introduce extreme distortions and noise in the…

Controlling nonlinear dynamical systems using machine learning allows to not only drive systems into simple behavior like periodicity but also to more complex arbitrary dynamics. For this, it is crucial that a machine learning system can be…

Reservoir computing is a neural network approach for processing time-dependent signals that has seen rapid development in recent years. Physical implementations of the technique using optical reservoirs have demonstrated remarkable accuracy…

Reservoir computing is a bio-inspired computing paradigm for processing time-dependent signals. Its hardware implementations have received much attention because of their simplicity and remarkable performance on a series of benchmark tasks.…

We consider discrete-time one-dimensional random dynamical systems with bounded noise, which generate an associated set-valued dynamical system. We provide necessary and sufficient conditions for a discontinuous bifurcation of a minimal…

We propose and demonstrate a nonlinear control method that can be applied to unknown, complex systems where the controller is based on a type of artificial neural network known as a reservoir computer. In contrast to many modern…

Reservoir Computing (RC) with physical systems requires an understanding of the underlying structure and internal dynamics of the specific physical reservoir. In this study, physical nano-electronic networks with neuromorphic dynamics are…

Double Hopf bifurcation analysis can be used to reveal some complicated dynamical behavior in a dynamical system, such as the existence or coexistence of periodic orbits, quasi-periodic orbits, or even chaos. In this paper, an algorithm for…

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…

Reduced-order dynamical models play a central role in developing our understanding of predictability of climate irrespective of whether we are dealing with the actual climate system or surrogate climate-models. In this context, the…