Aesthetics of Nonlinear World
A Recurrence-Based Network obtained from Rössler model:
Nonlinear Dynamics & Chaos
Nonlinear dynamical systems are usually defined by a set of nonlinear differential equations used for describing the time evolution of any kind of variables. Characterizing the behavior of such systems under different parameters and initial conditions is a task of major relevance in many scientific fields, including theoretical neuroscience or mathematical biology in a broader sense. In particular, the structure of the solution of such systems, the information transfer between nonlinear elements or even the phenomena of synchronization and pattern organization can be acessed by means of specific methematical metrics or techniques as the Lyapunov exponents, recurrence quantification analysis and information theory. I devote efforts for a better understading of nonlinear systems - specially neuronal systems - and such tools.  Some selected contributions are related to the topics:

  • Lyapunov exponents estimation for systems with a hard mathematical description (e.g. Hodgkin-Huxley model, multiscrolls models, etc);
  • Lagrangian Coherent Structures organization in nonlinear systems (neuronal systems and linear by parts models);
  • Information Transfer in Chaos-Based Communication Systems and in Neuronal Networks;
  • Recurrence Quantification Analysis (RQA) for blind source separation;
Some Selected Publications
Featured Publications:

•Finding specific oscillatory behavior based on Lyapunov spectrum;

•Chaotic behavior of Hodgkin-Huxley model under periodic forcing;

•Particle Swarm Optimization for minimizing the difference between Lyapunov spectrums

•A discussion about the relationship between the contributions of Alan Turing to the  field of artificial neural networks and reservoir computing is presented;

•The main points of contact between Turing’s ideas and these modern perspectives are outlined;

"Strange" Analog Neuron !
Strange attractor on FitzHugh-Nagumo analog neuronal model under periodic forcing
Biomedical Signal Processing & Instrumentation
Besides - and not decorrelated from nonlinear analysis -, I have worked on biomedical signal processing and biomedical instrumentation.  Some of these works are related to recurrence quantification analysis applications, analog circuits that simulate neuronal behavior, and, mainly, pattern recognition on Brain-Computer Interface (BCIs) systems.  BCIs systems outline alternative communication channels that aim to map directly brain signals to control commands for assistive devices. This is a quite exciting field for statistical modeling and learning many different processing strategies with a marvelous EEG application. Recently, we have also worked on mapping EMG signals to produce control signals for upper limb prosthesis.

  • Brain-Computer Interface systems;
  • Recurrence Quantification Analysis applied to Biomedical Signals 
  • Pattern recognition on EMG signals;
Some Selected Publications
Featured Publications:
•  We apply 36 scenarios of signal processing techniques for a same database of EEG-SSVEP;
•  Linear and nonlinear classifiers are analyzed, as LDA, SVM and ELM;
•  Analysis of different spectral features extraction techniques;
•  Comparison of distinct features selection strategies;
•  Statistical considerations about electrodes location;

If you looked it carefully and really wants to make part of these studies, please contact me. We have projects from undergraduate to postgraduate level on modeling nonlinear systems, time series analysis, Brain-Computer Interfaces, EEG and EMG signal processing and related biomedical instrumentation.

Thanks for being interested !!