Related papers: Dynamical analysis of a parameter-aware reservoir …
Forecasting chaotic systems is a notably complex task, which in recent years has been approached with reasonable success using reservoir computing (RC), a recurrent network with fixed random weights (the reservoir) used to extract the…
Reservoir computing systems are constructed using a driven dynamical system in which external inputs can alter the evolving states of a system. These paradigms are used in information processing, machine learning, and computation. A…
The objective of this paper is to study the dynamical behaviour systematically of an ecological system with Beddington-DeAngelis functional response which avoids the criticism occurred in the case of ratio-dependent functional response at…
We show how random feature maps can be used to forecast dynamical systems with excellent forecasting skill. We consider the tanh activation function and judiciously choose the internal weights in a data-driven manner such that the resulting…
Reservoir computing is a computational framework suited for temporal/sequential data processing. It is derived from several recurrent neural network models, including echo state networks and liquid state machines. A reservoir computing…
Multifunctionality is a well observed phenomenological feature of biological neural networks and considered to be of fundamental importance to the survival of certain species over time. These multifunctional neural networks are capable of…
Information processing abilities of active matter are studied in the reservoir computing (RC) paradigm to infer the future state of a chaotic signal. We uncover an exceptional regime of agent dynamics that has been overlooked previously. It…
We scrutinize the use of machine learning, based on reservoir computing, to build data-driven effective models of multiscale chaotic systems. We show that, for a wide scale separation, machine learning generates effective models akin to…
Quantifying the stability of an equilibrium is central in the theory of dynamical systems as well as in engineering and control. A comprehensive picture must include the response to both small and large perturbations, leading to the…
Reservoir computers (RCs) are powerful machine learning architectures for time series prediction. Recently, next generation reservoir computers (NGRCs) have been introduced, offering distinct advantages over RCs, such as reduced…
Nonlinear photonic sources including semiconductor lasers have recently been utilized as ideal computation elements for information processing. They supply energy-efficient way and rich dynamics for classification and recognition tasks. In…
The direct parametrisation method for invariant manifolds is adjusted to consider a varying parameter. More specifically, the case of systems experiencing a Hopf bifurcation in the parameter range of interest are investigated, and the…
Tipping points occur in many real-world systems, at which the system shifts suddenly from one state to another. The ability to predict the occurrence of tipping points from time series data remains an outstanding challenge and a major…
Many dynamical systems exhibit abrupt transitions or tipping as the control parameter is varied. In scenarios where the parameter is varied continuously, the rate of change of control parameter greatly affects the performance of early…
Bifurcation diagram is a powerful tool that visually gives information about the behavior of the equilibrium points of a dynamical system respect to the varying parameter. This paper proposes an educational algorithm by which the local…
Detecting early warning indicators for abrupt dynamical transitions in complex systems or high-dimensional observation data is essential in many real-world applications, such as brain diseases, natural disasters, and engineering…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
We study Hopfield networks with non-reciprocal coupling inducing switches between memory patterns. Dynamical phase transitions occur between phases of no memory retrieval, retrieval of multiple point-attractors, and limit-cycle attractors.…
A dynamical system that undergoes a supercritical Hopf's bifurcation is perturbed by a multiplicative Brownian motion that scales with a small parameter $\epsilon$. The random fluctuations of the system at the critical point are studied…
Bifurcations leading to complex dynamical behaviour of non-linear systems are often encountered when the characteristics of feedback circuits in the system are varied. In systems with many unknown or varying parameters, it is an…