Predicting Spatio-Temporal Time Series Using Dimension Reduced Local States

We present a method for both cross estimation and iterated time series prediction of spatio temporal dynamics based on reconstructed local states, PCA dimension reduction, and local modelling using nearest neighbour methods. The effectiveness of this approach is shown for (noisy) data from a (cubic) Barkley model, the Bueno-Orovio-Cherry-Fenton model, and the Kuramoto-Sivashinsky model

Estimating Lyapunov exponents in billiards

Dynamical billiards are paradigmatic examples of chaotic Hamiltonian dynamical systems with widespread applications in physics. We study how well their Lyapunov exponent, characterizing the chaotic dynamics, and its dependence on external parameters can be estimated from phase space volume arguments, with emphasis on billiards with mixed regular and chaotic phase spaces. We show that in the very diverse billiards considered here the leading contribution to the Lyapunov exponent is inversely proportional to the chaotic phase space volume, and subsequently discuss the generality of this relationship. We also extend the well established formalism by Dellago, Posch, and Hoover to calculate the Lyapunov exponents of billiards to include external magnetic fields and provide a software implementation of it

TimeseriesSurrogates.jl: a Julia package for generating surrogate data

publishedVersio

Predicting Spatio-Temporal Time Series Using Dimension Reduced Local States

We present a method for both cross estimation and iterated time series prediction of spatio temporal dynamics based on reconstructed local states, PCA dimension reduction, and local modelling using nearest neighbour methods. The effectiveness of this approach is shown for (noisy) data from a (cubic) Barkley model, the Bueno-Orovio-Cherry-Fenton model, and the Kuramoto-Sivashinsky model

Framework for global stability analysis of dynamical systems

Dynamical systems, that are used to model power grids, the brain, and other physical systems, can exhibit coexisting stable states known as attractors. A powerful tool to understand such systems, as well as to better predict when they may ``tip'' from one stable state to the other, is global stability analysis. It involves identifying the initial conditions that converge to each attractor, known as the basins of attraction, measuring the relative volume of these basins in state space, and quantifying how these fractions change as a system parameter evolves. By improving existing approaches, we present a comprehensive framework that allows for global stability analysis on any dynamical system. Notably, our framework enables the analysis to be made efficiently and conveniently over a parameter range. As such, it becomes an essential complement to traditional continuation techniques, that only allow for linear stability analysis. We demonstrate the effectiveness of our approach on a variety of models, including climate, power grids, ecosystems, and more. Our framework is available as simple-to-use open-source code as part of the DynamicalSystems.jl library

Agents.jl: A performant and feature-full agent based modelling software of minimal code complexity

Agent based modelling is a simulation method in which autonomous agents interact with their environment and one another, given a predefined set of rules. It is an integral method for modelling and simulating complex systems, such as socio-economic problems. Since agent based models are not described by simple and concise mathematical equations, code that generates them is typically complicated, large, and slow. Here we present Agents.jl, a Julia-based software that provides an ABM analysis platform with minimal code complexity. We compare our software with some of the most popular ABM software in other programming languages. We find that Agents.jl is not only the most performant, but also the least complicated software, providing the same (and sometimes more) features as the competitors with less input required from the user. Agents.jl also integrates excellently with the entire Julia ecosystem, including interactive applications, differential equations, parameter optimization, and more. This removes any ``extensions library'' requirement from Agents.jl, which is paramount in many other tools