Related papers: Basins of Attraction: A Dynamical Zoo
The basin entropy is a simple idea that aims to measure the the final state unpredictability of multistable systems. Since 2016, the basin entropy has been widely used in different contexts of physics, from cold atoms to galactic dynamics.…
The Mackey-Glass system is a paradigmatic example of a delayed model whose dynamics is particularly complex due to, among other factors, its multistability involving the coexistence of many periodic and chaotic attractors. The prediction of…
A recurrent neural network is considered that can retrieve a collection of patterns, as well as slightly perturbed versions of this `pure' set of patterns via fixed points of its dynamics. By replacing the set of dynamical constraints,…
There are many natural, physical, and biological systems that exhibit multiple time scales. For example, the dynamics of a population of ticks can be described in continuous time during their individual life cycle yet discrete time is used…
Dynamical systems that describe the escape from the basins of attraction of stable invariant sets are presented and analyzed. It is shown that the stable fixed points of such dynamical systems are the index-1 saddle points. Generalizations…
In this paper, we study geometric properties of basins of attraction of monotone systems. Our results are based on a combination of monotone systems theory and spectral operator theory. We exploit the framework of the Koopman operator,…
Chaotic dynamical systems with two or more attractors lying on invariant subspaces may, provided certain mathematical conditions are fulfilled, exhibit intermingled basins of attraction: Each basin is riddled with holes belonging to basins…
In this work, we numerically investigate and visually illustrate the dynamical properties of the dissipative spin-orbit problem such as the co-existence of multiple periodic and quasi-periodic attractors, and the complexity of the…
Systems with many stable configurations abound in nature, both in living and inanimate matter. Their inherent nonlinearity and sensitivity to small perturbations make them challenging to study, particularly in the presence of external…
This essay provides a critical overview of the mathematical kinetic theory of active particles, which is used to model and study collective systems consisting of interacting living entities, such as those involved in behavior and evolution.…
Multiple stable states - the coexistence of two or more distinct ecological configurations under identical environmental conditions - have attracted sustained interest in ecology, yet the field still lacks a unified framework connecting…
A computationally simple way to accommodate 'basins' of trapping sites in standard kinetic Monte Carlo simulations is presented. By assuming the system is effectively equilibrated in the basin, the residence time (time spent in the basin…
In this paper, we examine the relationship between the stability of the dynamical system $x^{\prime}=f(x)$ and the computability of its basins of attraction. We present a computable $C^{\infty}$ system $x^{\prime}=f(x)$ that possesses a…
The attractors of Boolean networks and their basins have been shown to be highly relevant for model validation and predictive modelling, e.g., in systems biology. Yet there are currently very few tools available that are able to compute and…
Power systems dominated by renewable energy encounter frequently large, random disturbances, and a critical challenge faced in power-system management is how to anticipate accurately whether the perturbed systems will return to the…
Multifunctionality is ubiquitous in biological neurons. Several studies have translated the concept to artificial neural networks as well. Recently, multifunctionality in reservoir computing (RC) has gained the widespread attention of…
Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which \textit{unstable…
Two-dimensional maps can model interactions between populations. Despite their simplicity, these dynamical systems can show some complex situations, as multistability or fractal boundaries between basins that lead to remarkable pictures.…
We propose a methodology to analyze synchronization in an ensemble of diffusively coupled multistable systems. First, we study how two bidirectionally coupled multistable oscillators synchronize and demonstrate the high complexity of the…
Rich out of equilibrium collective dynamics of strongly interacting large assemblies emerge in many areas of science. Some intriguing and not fully understood examples are the glassy arrest in atomic, molecular or colloidal systems,…