Examinando por Autor "Wagemakers, Alexandre"

Mostrando 1 - 20 de 43

A Spatial Time-Frequency Hopping Index Modulated Scheme in Turbulence-free Optical Wireless Communication Channels
(Institute of Electrical and Electronics Engineers, 2020-07-01) Escribano, Francisco J.; Wagemakers, Alexandre; Kaddoum, Georges; Evangelista, Joao V. C.
A test for fractal boundaries based on the basin entropy
(Elsevier, 2020-10-31) Puy, Andreu; Daza, Alvar; Wagemakers, Alexandre; Sanjuán, Miguel AF
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 unpredictability in the final state of a system when there is an initial perturbation or uncertainty in the initial state. Based on the basin entropy, the log2 criterion allows for efficient testing of fractal basin boundaries at a fixed resolution. Here, we extend this criterion into a new test with improved sensitivity that we call the fractality test. Using the same single scale information, the fractality test allows for the detection of fractal boundaries in many more cases than the log2 criterion. The new test is illustrated with the paradigmatic driven Duffing oscillator, and the results are compared with the classical approach given by the uncertainty exponent. We believe that this work can prove particularly useful to study both high-dimensional systems and experimental basins of attraction.
Ascertaining when a basin is Wada: the merging method
(Nature, 2018-07-02) Daza, Alvar; Wagemakers, Alexandre; Sanjuán, Miguel A. F.
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 present a new perspective on the Wada property: A Wada boundary is the only one that remains unaltered under the action of merging the basins. This observation allows to develop a new method to test the Wada property, which is much faster than the previous ones. Furthermore, another major advantage of the merging method is that a detailed knowledge of the dynamical system is not required.
Basin entropy: a new tool to analyze uncertainty in dynamical systems
(Nature, 2016-08-12) Daza, Alvar; Wagemakers, Alexandre; Georgeot, Bertrand; Guéry-Odelin, David; Sanjuán, Miguel A. F.
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 several outcomes are possible, which is a common situation in neuroscience, economy, astronomy, ecology and many other disciplines. Depending on the nature of the basins, prediction can be difficult even in systems that evolve under deterministic rules. From this respect, a proper classification of this unpredictability is clearly required. To address this issue, we introduce the basin entropy, a measure to quantify this uncertainty. Its application is illustrated with several paradigmatic examples that allow us to identify the ingredients that hinder the prediction of the final state. The basin entropy provides an efficient method to probe the behavior of a system when different parameters are varied. Additionally, we provide a sufficient condition for the existence of fractal basin boundaries: when the basin entropy of the boundaries is larger than log2, the basin is fractal.
Building electronic bursters with the morris–lecar neuron model
(World Scientific Publishing, 2006-01-18) Wagemakers, Alexandre; Sanjuán, Miguel A.F.; Casado, José M.; Aihara, Kazuyuki
We propose a method for the design of electronic bursting neurons, based on a simple conductance neuron model. A burster is a particular class of neuron that displays fast spiking regimes alternating with resting periods. Our method is based on the use of an electronic circuit that implements the well-known Morris–Lecar neuron model. We use this circuit as a tool of analysis to explore some regions of the parameter space and to contruct several bifurcation diagrams displaying the basic dynamical features of that system. These bifurcation diagrams provide the initial point for the design and implementation of electronic bursting neurons. By extending the phase space with the introduction of a slow driving current, our method allows to exploit the bistabilities which are present in the Morris–Lecar system to the building of different bursting models.
Chaos-Based Multicarrier VLC Modulator With Compensation of LED Nonlinearity
(2019-01-10) Escribano, Francisco J.; Sáez-Landete, José; Wagemakers, Alexandre
Chaos-Based Turbo Systems in Fading Channels
(IEEE, 2014-02-01) Escribano, Francisco J.; Wagemakers, Alexandre; Sanjuán, Miguel A. F.
Chaotic dynamics and fractal structures in experiments with cold atoms
(APS, 2017-01-25) Daza, Alvar; Georgeot, Bertrand; Guéry-Odelin, David; Wagemakers, Alexandre; Sanjuán, Miguel A. F.
We exploit tools from nonlinear dynamics to the detailed analysis of cold atom experiments. A powerful example is provided by the recent concept of basin entropy which allows to quantify the final state unpredictability that results from the complexity of the phase space geometry. We show here that this enables one to reliably infer the presence of fractal structures in phase space from direct measurements. We exemplify the method with numerical simulations in an experimental configuration made of two crossing laser guides and originally used as a matter wave splitter.
Characterization of Fractal Basins Using Deep Convolutional Neural Networks
(International Journal of Bifurcation and Chaos, 2022-07-12) Valle, David; Wagemakers, Alexandre; Daza, Alvar; Sanjuán, Miguel A.F.
Neural network models have recently demonstrated impressive prediction performance in complex systems where chaos and unpredictability appear. In spite of the research efforts carried out on predicting future trajectories or improving their accuracy compared to numerical methods, not sufficient work has been done on using deep learning techniques in which the unpredictability can be characterized of chaotic systems or give a general view of the global unpredictability of a system. In this work, we propose a novel approach based on deep learning techniques to measure the fractal dimension of the basins of attraction of the Duffing oscillator for a variety of parameters. As a consequence, we provide an algorithm capable of predicting fractal dimension measures as accurately as the box-counting algorithm, but with a computation speed about ten times faster.
Classifying basins of attraction using the basin entropy
(Elsevier, 2022) Daza, Alvar; Wagemakers, Alexandre; Fernandez Sanjuán, Miguel A.
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 common basins found in nonlinear dynamics with the help of the basin entropy. We have also found interesting connections between the basin entropy and other measures used to characterize the unpredictability associated to the basins of attraction, such as the uncertainty exponent, the lacunarity or other different parameters related to the Wada property.
Controlling transient chaos in the Lorenz system with machine learning
(Springer, 2025-03-28) Valle, David; Capeáns, Ruben; Wagemakers, Alexandre; Sanjuán, Miguel A. F.
This paper presents a novel approach to sustain transient chaos in the Lorenz system through the estimation of safety functions using a transformer-based model. Unlike classical methods that rely on iterative computations, the proposed model directly predicts safety functions without requiring finetuning or extensive system knowledge. The results demonstrate that this approach effectively maintains chaotic trajectories within the desired phase space region, even in the presence of noise, making it a viable alternative to traditional methods. A detailed comparison of safety functions, safe sets, and their control performance highlights the strengths and trade-offs of the two approaches.
Cyclic motifs as the governing topological factor in time-delayed oscillator networks
(APS, 2014-11-24) Nordenfelt, Anders; Wagemakers, Alexandre; Sanjuán, Miguel A. F.
We identify the relative amount of short cyclic motifs as an important topological factor in networks of time delayed Kuramoto oscillators. The patterns emerging from the cyclic motifs are most clearly distinguishable in the average frequency and the momentary frequency dispersion as a function of the time delay. In particular, the common distinction between bi-directional and unidirectional couplings is shown to have a decisive effect on the network dynamics. We argue that the behavior peculiar to the sparsely connected uni-directional random network can be described essentially as the lack of distinguishable patterns originating from cyclic motifs of any specific length.
Deep learning-based analysis of basins of attraction
(American Institute of Physics, 2024-03-04) Valle, David; Wagemakers, Alexandre; Sanjuán, Miguel A.F.
This research addresses the challenge of characterizing the complexity and unpredictability of basins within various dynamical systems. The main focus is on demonstrating the efficiency of convolutional neural networks (CNNs) in this field. Conventional methods become computationally demanding when analyzing multiple basins of attraction across different parameters of dynamical systems. Our research presents an innovative approach that employs CNN architectures for this purpose, showcasing their superior performance in comparison to conventional methods. We conduct a comparative analysis of various CNN models, highlighting the effectiveness of our proposed characterization method while acknowledging the validity of prior approaches. The findings not only showcase the potential of CNNs but also emphasize their significance in advancing the exploration of diverse behaviors within dynamical systems.
Design ad Performance Analysis of an Index Time-Frequency Modulation Scheme for Optical Communications
(IEEE, 2019-10-01) Escribano, Francisco J.; Wagemakers, Alexandre; Kaddoum, Georges; Evangelista, Joao V. C.
In this article, we propose an index modulation system suitable for optical communications, based on jointly driving the time and frequency of the signal: an index-time frequency hopping (I-TFH) system. We analyze its performance from the point of view of its efficiency in power and spectrum, and its behavior in terms of error probability for the non- turbulent free-space optical (FSO) channel. We compare I-TFH with already proposed index modulated systems of the same nature, but where the amplitude or the number of transmitters are driven instead of the signal frequency.We derive and compare approximations for the average symbol and bit error probabilities of all these systems. The simulation results show that said approximations are tight enough for a wide range of signal-to- noise ratios and system parameters. Moreover, I-TFH shows to be better performing in BER and/or power efficiency than the comparative alternatives, and may offer interesting properties in a variety of contexts.
Design of a New Differential Chaos-Shift-Keying System for Continuous Mobility
(IEEE, 2016-05-02) Escribano, Francisco J.; Kaddoum, Georges; Wagemakers, Alexandre; Giard, Pascal
Effortless estimation of basins of attraction
(2022-02-01) Datseris, George; Wagemakers, Alexandre
We present a fully automated method that identifies attractors and their basins of attraction without approximations of the dynamics. The method works by defining a finite state machine on top of the dynamical system flow. The input to the method is a dynamical system evolution rule and a grid that partitions the state space. No prior knowledge of the number, location, or nature of the attractors is required. The method works for arbitrarily high-dimensional dynamical systems, both discrete and continuous. It also works for stroboscopic maps, Poincaré maps, and projections of high-dimensional dynamics to a lower-dimensional space. The method is accompanied by a performant open-source implementation in the DynamicalSystems.jl library. The performance of the method outclasses the naïve approach of evolving initial conditions until convergence to an attractor, even when excluding the task of first identifying the attractors from the comparison. We showcase the power of our implementation on several scenarios, including interlaced chaotic attractors, high-dimensional state spaces, fractal basin boundaries, and interlaced attracting periodic orbits, among others. The output of our method can be straightforwardly used to calculate concepts, such as basin stability and final state sensitivity.
Electronic Design Of Synthetic Genetic Networks
(International Journal of Bifurcation and Chaos, 2007-10-01) Buldú, Javier; García-Ojalvo, Jordi; Wagemakers, Alexandre; Sanjuán, Miguel A. F.
We propose the use of nonlinear electronic circuits to study synthetic gene regulation networks. Specifically, we have designed two electronic versions of a synthetic genetic clock, known as the "repressilator," making use of appropriate electronic elements linked in the same way as the original biochemical system. We study the effects of coupling in a population of electronic repressilators, with the aim of observing coherent oscillations of the whole population. With these results, we show that this kind of nonlinear circuits can be helpful in the design and understanding of synthetic genetic networks.
Entraining synthetic genetic oscillators
(American Institute of Physics, 2009-09-17) Wagemakers, Alexandre; Buldú, J.M.; Sanjuán, M.A.F.; Luis, O. de; Izquierdo, A.; Coloma, Antonio
We propose a new approach for synchronizing a population of synthetic genetic oscillators, which consists in the entrainment of a colony of repressilators by external modulation. We present a model where the repressilator dynamics is affected by periodic changes in temperature. We introduce an additional plasmid in the bacteria in order to correlate the temperature variations with the enhancement of the transcription rate of a certain gene. This can be done by introducing a promoter that is related to the heat shock response. This way, the expression of that gene results in a protein that enhances the overall oscillations. Numerical results show coherent oscillations of the population for a certain range of the external frequency, which is in turn related to the natural oscillation frequency of the modified repressilator. Finally we study the transient times related with the loss of synchronization and we discuss possible applications in biotechnology of large-scale production coupled to synchronization events induced by heat shock.
Experimental demonstration of bidirectional chaotic communication by means of isochronal synchronization
(IOP Publishing ; EPL Association, 2008-01-21) Wagemakers, Alexandre; Buldú, Javier M.; Sanjuán, Miguel A.F.
We give the first experimental demonstration of simultaneous bidirectional communication through chaotic carriers thanks to the phenomenon of isochronal synchronization. Two Mackey-Glass electronic circuits with chaotic behaviour exchange their signals through a coupling line with delay. When the internal feedback of the circuits and the coupling are accurately matched, isochronal synchronization arises. Under this dynamical regime, we introduce a binary message at both outputs and recover it at the opposite circuit. Finally, we discuss the security of this kind of communication system by analyzing the message recovered by a potential eavesdropper.
Framework for global stability analysis of dynamical systems
(2023-07-01) Datseris, George; Luiz Rossi, Kalel; Wagemakers, Alexandre
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 of dynamical systems. Notably, our framework enables the analysis to be made efficiently and conveniently over a parameter range. As such, it becomes an essential tool for stability analysis of dynamical systems that goes beyond local stability analysis offered by alternative frameworks. 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.