Browsing by Autor "Jason A. C. Gallas"

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Análisis del plano de fases de un modelo discreto de neurona basado en la determinación de periodicidades
(2015) G. M Ramírez Ávila; Márcia Russman Gallas; Jason A. C. Gallas
AUTOSIMILARIDADES EN EL ESPACIO DE PARÁMETROS DEL CIRCUITO DE CHUA CON NO-LINEALIDADES DISCRETAS Y CONTINUAS
(2011) Gonzalo Marcelo Ramírez-Ávila; Jason A. C. Gallas
Se muestran autosimilaridades en el espacio de par´ametros del circuito de Chua tanto con una no-linealidad discontinua como con una no-linealidad c ´ubica. Mediante un an´alisis sencillo de estas estructuras, se calcula de manera aproximada sus dimensiones fractales
CARACTERIZACIÓN DE SISTEMAS DINÁMICOS MEDIANTE PERIODICIDADES
(2011) Gonzalo Marcelo Ramírez-Ávila; Jason A. C. Gallas
We characterize, by means of periodicities, some dynamical systems represented by maps. This is an alternative method to the common bifurcation diagrams computed by using the Lyapunov exponents and allows us to visualize the typical structures onto the parameter space such as the “shrimps” but in addition with the detail of the oscillatory regimes which could be important from a practical viewpoint.
Distribution of spiking and bursting in Rulkov’s neuron model
(Springer Science+Business Media, 2022) Gonzalo Marcelo Ramírez-Ávila; Stéphanie Depickère; Imre M. Jánosi; Jason A. C. Gallas
Abstract Large-scale brain simulations require the investigation of large networks of realistic neuron models, usually represented by sets of differential equations. Here we report a detailed fine-scale study of the dynamical response over extended parameter ranges of a computationally inexpensive model, the two-dimensional Rulkov map, which reproduces well the spiking and spiking-bursting activity of real biological neurons. In addition, we provide evidence of the existence of nested arithmetic progressions among periodic pulsing and bursting phases of Rulkov’s neuron. We find that specific remarkably complex nested sequences of periodic neural oscillations can be expressed as simple linear combinations of pairs of certain basal periodicities. Moreover, such nested progressions are robust and can be observed abundantly in diverse control parameter planes which are described in detail. We believe such findings to add significantly to the knowledge of Rulkov neuron dynamics and to be potentially helpful in large-scale simulations of the brain and other complex neuron networks.
ESTRUCTURA DEL ESPACIO DE PARÁMETROS PARA LAS ECUACIONES DEL CIRCUITO DE CHUA
(2008) Gonzalo Marcelo Ramírez-Ávila; Jason A. C. Gallas
We study in detail the parameter space for nonlinear differential equations corresponding to the Chua’s circuit. Our analysis of two and three parameters confirms preliminary results obtained in [1]. In addition, it shows the existence of structures denoting periodicities called “shrimps” and a hub which organizes these structuresinto “spirals”.
How community size affects survival chances in cyclic competition games that microorganisms play
(American Physical Society, 2010) Ana Paula Oliveira Muller; Jason A. C. Gallas
Cyclic competition is a mechanism underlying biodiversity in nature and the competition between large numbers of interacting individuals under multifaceted environmental conditions. It is commonly modeled with the popular children's rock-paper-scissors game. Here we probe cyclic competition systematically in a community of three strains of bacteria Escherichia coli. Recent experiments and simulations indicated the resistant strain of E. coli to win the competition. Other data, however, predicted the sensitive strain to be the final winner. We find a generic feature of cyclic competition that solves this puzzle: community size plays a decisive role in selecting the surviving competitor. Size-dependent effects arise from an easily detectable "period of quasiextinction" and may be tested in experiments. We briefly indicate how.
How similar is the performance of the cubic and the piecewise-linear circuits of Chua?
(Elsevier BV, 2010) Gonzalo Marcelo Ramírez-Ávila; Jason A. C. Gallas
Ubiquity of ring structures in the control space of complex oscillators
(American Institute of Physics, 2021) Gonzalo Marcelo Ramírez-Ávila; Jürgen Kurths; Jason A. C. Gallas
We report the discovery of two types of stability rings in the control parameter space of a vertical-cavity surface-emitting semiconductor laser. Stability rings are closed parameter paths in the laser control space. Inside such rings, laser stability thrives even in the presence of small parameter fluctuations. Stability rings were also found in rather distinct contexts, namely, in the way that cancerous, normal, and effector cells interact under ionizing radiation and in oscillations of an electronic circuit with a junction-gate field-effect transistor (JFET) diode. We argue that stability-enhancing rings are generic structures present in the control parameter space of many complex systems.