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- Cristian Bonatto, Jason Alfredo Carlson Gallas
- Philosophical transactions. Series A…
- 2008

We report high-resolution phase diagrams for several familiar dynamical systems described by sets of ordinary differential equations: semiconductor lasers; electric circuits; Lorenz-84 low-order atmospheric circulation model; and Rössler and chemical oscillators. All these systems contain chaotic phases with highly complicated and interesting accumulation… (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)

- D R Paula, A D Araújo, J S Andrade, H J Herrmann, J 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)

- Paulo Cesar Rech, Marcus Werner Beims, Jason A C Gallas
- Physical review. E, Statistical, nonlinear, and…
- 2005

Recent methods for stabilizing systems like, e.g., loss-modulated CO2 lasers, involve inducing controlled monostability via slow parameter modulations. However, such stabilization methods presuppose detailed knowledge of the structure and size of basins of attraction. In this Brief Report, we numerically investigate basin size evolution when parameters are… (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)

- 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)

- R. Stoop, J. C. Gallas, A. Kern
- 2005

Cochlear two-tone suppression is the dominant contrast-sharpening phenomenon of hearing and provides a decisive test for the correct implementation of hearing nonlinearities in models of the cochlea. Although critically tuned Hopf amplifiers were shown recently to be fruitful models of intricate phenomena in the physiology of the human ear, we find that… (More)

- Ana Paula O Müller, Jason A C Gallas
- Physical review. E, Statistical, nonlinear, and…
- 2010

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… (More)

- Luciano Camargo Martins, Jason Alfredo Carlson Gallas
- I. J. Bifurcation and Chaos
- 2008

We investigate the prevalence of multistability in the parameter space of the kicked rotor map. We report high-resolution phase diagrams showing how the density of attractors and the density of periods vary as a function of both model parameters. Our diagrams illustrate density variations that exist when moving between the familiar conservative and strongly… (More)

- Marcus W. Beims, Jason A. C. Gallas
- Scientific reports
- 2016

Chaos and regularity are routinely discriminated by using Lyapunov exponents distilled from the norm of orthogonalized Lyapunov vectors, propagated during the temporal evolution of the dynamics. Such exponents are mean-field-like averages that, for each degree of freedom, squeeze the whole temporal evolution complexity into just a single number. However,… (More)