205 citations · 379 across the 15 of their papers we have counts for
12 papers · 1 filter
Bayesian Basin Tracking: Efficient Global Continuation of Multistable Dynamical Systems
Pedro Haerter, Alexandre Wagemakers, Alvar Daza +1
Mapping the global phase space of high-dimensional multistable dynamical systems is computationally prohibitive because conventional approaches require extensive numerical integrat…
Characterization of Fractal Basins Using Deep Convolutional Neural Networks
David Valle, Alexandre Wagemakers, Alvar Daza +1
Neural network models have recently demonstrated impressive prediction performance in complex systems where chaos and unpredictability appear. In spite of the research efforts carr…
Using the basin entropy to explore bifurcations
Alexandre Wagemakers, Alvar Daza, Miguel A. F. Sanjuán
Bifurcation theory is the usual analytic approach to study the parameter space of a dynamical system. Despite the great power of prediction of these techniques, fundamental limitat…
Unpredictability and basin entropy
Alvar Daza, Alexandre Wagemakers, Miguel A. F. Sanjuán
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…
A test for fractal boundaries based on the basin entropy
Andreu Puy, Alvar Daza, Alexandre Wagemakers +1
In dynamical systems, basins of attraction connect a given set of initial conditions in phase space to their asymptotic states. The basin entropy and related tools quantify the unp…
Classifying basins of attraction using the basin entropy
Alvar Daza, Alexandre Wagemakers, Miguel A. F. Sanjuán
A basin of attraction represents the set of initial conditions leading to a specific asymptotic state of a given dynamical system. Here, we provide a classification of the most com…
How to detect Wada Basins
Alexandre Wagemakers, Alvar Daza, Miguel A. F. Sanjuan
We present a review of the different techniques available to study a special kind of fractal basins of attraction known as Wada basins, which have the intriguing property of having…
The saddle-straddle method to test for Wada basins
Alexandre Wagemakers, Alvar Daza, Miguel A. F. Sanjuán
First conceived as a topological construction, Wada basins abound in dynamical systems. Basins of attraction showing the Wada property possess the particular feature that any small…
Computing complex horseshoes by means of piecewise maps
Álvaro G. López, Álvar Daza, Jesús M. Seoane +1
A systematic procedure to numerically compute a horseshoe map is presented. This new method uses piecewise functions and expresses the required operations by means of elementary tr…
Ascertaining when a basin is Wada: the merging method
Alvar Daza, Alexandre Wagemakers, Miguel A. F. Sanjuán
Trying to imagine three regions separated by a unique boundary seems a difficult task. However, this is exactly what happens in many dynamical systems showing Wada basins. Here, we…
Wada property in systems with delay
Alvar Daza, Alexandre Wagemakers, Miguel A. F. Sanjuán
Delay differential equations take into account the transmission time of the information. These delayed signals may turn a predictable system into chaotic, with the usual fractaliza…
Basin entropy: a new tool to analyze uncertainty in dynamical systems
Alvar Daza, Alexandre Wagemakers, Bertrand Georgeot +2
In nonlinear dynamics, basins of attraction link a given set of initial conditions to its corresponding final states. This notion appears in a broad range of applications where sev…