Recurrent neural networks have recently proved the state-of-the-art approach in forecasting
complex oscillatory time series on a multi-step horizon. Researchers in the field investigated …

This book aims to present a new approach called Flow Curvature Method that applies
Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any …

The aim of this article is to highlight the interest to apply Differential Geometry and
Mechanics concepts to chaotic dynamical systems study. Thus, the local metric properties of …

In this paper, a new stochastic phenomenon of the noise-induced shift of random states of
the stochastically forced system into the domain of the phase plane where the original …

This work presents an efficient approach for computing the slow invariant manifold of the
fourth-order canonical memristor-based Chua circuits using the flow curvature method. First …

Considering trajectory curves, integral of n-dimensional dynamical systems, within the
framework of Differential Geometry as curves in Euclidean n-space, it will be established in …

Recurrent neural networks (RNN) as used in machine learning are commonly formulated in
discrete time, ie as recursive maps. This brings a lot of advantages for training models on …

Slow–fast dynamical systems, ie singularly or nonsingularly perturbed dynamical systems
possess slow invariant manifolds on which trajectories evolve slowly. Since the last century …

The forced van der Pol equation was introduced in the 1920s as a model of an electrical
circuit. Cartwright and Littlewood established the existence of invariant sets with complex …

During this last decades, several attempts to construct slow invariant manifold of the Lorenz–
Krishnamurthy five-mode model of slow–fast interactions in the atmosphere have been …