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- Pedro G. Lind, Jason A. C. Gallas, Hans J. Herrmann
- Physical review. E, Statistical, nonlinear, and…
- 2004

We study fully synchronized states in scale-free networks of chaotic logistic maps as a function of both dynamical and topological parameters. Three different network topologies are considered: (i) a random scale-free topology, (ii) a deterministic pseudofractal scale-free network, and (iii) an Apollonian network. For the random scale-free topology we find… (More)

- Joana G. Freire, Jason A. C. Gallas
- Physical chemistry chemical physics : PCCP
- 2011

We investigate the distribution of mixed-mode oscillations in the control parameter space for two paradigmatic chemical models: a three-variable fourteen-parameter model of the Belousov-Zhabotinsky reaction and a three-variable four-parameter autocatalator. For both systems, several high-resolution phase diagrams show that the number of spikes of their… (More)

- Jason A. C. Gallas
- I. J. Bifurcation and Chaos
- 2010

This manuscript reports numerical investigations about the relative abundance and structure of chaotic phases in autonomous dissipative flows, i.e. in continuous-time dynamical systems described by sets of ordinary differential equations. In the first half, we consider flows containing “periodicity hubs”, which are remarkable points responsible for… (More)

- Cristian Bonatto, Jean Claude Garreau, Jason A. C. Gallas
- Physical review letters
- 2005

We show the standard two-level continuous-time model of loss-modulated CO2 lasers to display the same regular network of self-similar stability islands known so far to be typically present only in discrete-time models based on mappings. Our results suggest that the two-parameter space of class B laser models and that of a certain class of discrete mappings… (More)

- Cristian Bonatto, Jason A. C. Gallas
- Physical review. E, Statistical, nonlinear, and…
- 2007

We study the hierarchical structuring of islands of stable periodic oscillations inside chaotic regions in phase diagrams of single-mode semiconductor lasers with optical injection. Phase diagrams display remarkable accumulation horizons: boundaries formed by the accumulation of infinite cascades of self-similar islands of periodic solutions of… (More)

- Cristian Bonatto, Jason A. C. Gallas
- Physical review letters
- 2008

We report the discovery of a remarkable "periodicity hub" inside the chaotic phase of an electronic circuit containing two diodes as a nonlinear resistance. The hub is a focal point from where an infinite hierarchy of nested spirals emanates. By suitably tuning two reactances simultaneously, both current and voltage may have their periodicity increased… (More)

- Cristian Bonatto, Jason A. C. Gallas, Yoshisuke Ueda
- Physical review. E, Statistical, nonlinear, and…
- 2008

We report strong evidence of remarkably close periodic repetitions of the structuring of the parameter space of a damped-driven Duffing oscillator as the amplitude of the drive increases. Families of period-adding cascades and some intricate networks of periodic oscillations embedded in chaotic phases are also found to recur closely as the driving force… (More)

- Renato Vitolo, Paul Glendinning, Jason A. C. Gallas
- Physical review. E, Statistical, nonlinear, and…
- 2011

Infinite cascades of periodicity hubs were predicted and very recently observed experimentally to organize stable oscillations of some dissipative flows. Here we describe the global mechanism underlying the genesis and organization of networks of periodicity hubs in control parameter space of a simple prototypical flow, namely a Rössler's oscillator. We… (More)

- Demétrius R Paula, Ascânio D. Araújo, José S. Andrade, Hans J. Herrmann, Jason A. C. Gallas
- Physical review. E, Statistical, nonlinear, and…
- 2006

We study a model for neural activity on the small-world topology of Watts and Strogatz and on the scale-free topology of Barabási and Albert. We find that the topology of the network connections may spontaneously induce periodic neural activity, contrasting with nonperiodic neural activities exhibited by regular topologies. Periodic activity exists only for… (More)

- Joana G. Freire, Richard J. Field, Jason A. C. Gallas
- The Journal of chemical physics
- 2009

We report a detailed numerical investigation of the relative abundance of periodic and chaotic oscillations in phase diagrams for the Belousov-Zhabotinsky (BZ) reaction as described by a nonpolynomial, autonomous, three-variable model suggested by Gyorgyi and Field [Nature (London) 355, 808 (1992)]. The model contains 14 parameters that may be tuned to… (More)