Jason A. C. Gallas

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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)
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)
We study the dynamics of patterns exhibited by rule 52, a totalistic cellular automaton displaying intricate behaviors and wide regions of active/inactive synchronization patches. Systematic computer simulations involving 2(30) initial configurations reveal that all complexity in this automaton originates from random juxtaposition of a very small number of(More)
We present a study of ocean convection parameterization based on a novel approach which includes both eddy diffusion and advection and consists of a two-dimensional lattice of bistable maps. This approach retains important features of usual grid models and allows to assess the relative roles of diffusion and advection in the spreading of convective cells.(More)
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)
We report the experimental discovery of a remarkable organization of the set of self-generated periodic oscillations in the parameter space of a nonlinear electronic circuit. When control parameters are suitably tuned, the wave pattern complexity of the periodic oscillations is found to increase orderly without bound. Such complex patterns emerge forming(More)
This paper reports histograms showing the detailed distribution of periodic and aperiodic motions in parameter-space of one-dimensional lattices of diffusively coupled quadratic maps subjected to periodic boundary conditions. Particular emphasis is given to the parameter domains where lattices support traveling patterns.
The investigation of regular and irregular patterns in nonlinear oscillators is an outstanding problem in physics and in all natural sciences. In general, regularity is understood as tantamount to periodicity. However, there is now a flurry of works proving the existence of "antiperiodicity", an unfamiliar type of regularity. Here we report the experimental(More)
a r t i c l e i n f o a b s t r a c t Computer simulations of complex spatio-temporal patterns using cellular automata may be performed in two alternative ways, the better choice depending on the relative size between the spatial width W of the expected patterns and their corresponding temporal period T. While the traditional timewise updating algorithm is(More)