Jason A. C. Gallas

Self-Similarities in the Frequency-Amplitude Space of a Loss-Modulated CO2 Laser

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 could be isomorphic.

Dissecting shrimps: results for some one-dimensional physical models

This paper describes how certain shrimp-like clusters of stability organize themselves in the parameter space of dynamical systems. Clusters are composed of an infinite affine-similar repetition of a basic elementary cell containing two primay noble points, a head and a tail, defining an axis of approximate symmetry. Knowledge of the axis and the skewness of the k-periodic main cell of k×2n cluster is enough to define the orientation of the whole cluster in space. Peculiarly simple directions along which shrimp-like clusters align are formed by the locus of doubly degenerate saddle zero multipliers corresponding to the main shrimp head. In addition, we report a family of models having the boundaries of all isoperiodic domains of stability totally degenerate and describe different aspects of their mathematical arrangement and some of their consequences for example, that shrimps are diffeomorphic copies of shrimps.

Accumulation horizons and period adding in optically injected semiconductor lasers

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 ever-increasing period. Each cascade follows a specific period-adding route. The riddling of chaotic laser phases by such networks of periodic solutions may compromise applications operating with chaotic signals such as, e.g., secure communications.

Coherence in scale-free networks of chaotic maps

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 a coupling strength threshold beyond which full synchronization is attained. This threshold scales as k(-mu) , where k is the outgoing connectivity and mu depends on the local nonlinearity. For deterministic scale-free networks coherence is observed only when the coupling strength is proportional to the neighbor connectivity. We show that the transition to coherence is of first order and study the role of the most connected nodes in the collective dynamics of oscillators in scale-free networks.

Relative abundance and structure of chaotic behavior: the nonpolynomial Belousov-Zhabotinsky reaction kinetics.

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 produce rich dynamical scenarios. By computing the Lyapunov spectra, we find the structuring of periodic and chaotic phases of the BZ reaction to display unusual global patterns, very distinct from those recently found for gas and semiconductor lasers, for electric circuits, and for a few other familiar nonlinear oscillators. The unusual patterns found for the BZ reaction are surprisingly robust and independent of the parameter explored.

Molecular dynamics simulation of size segregation in three dimensions

We report the first three-dimensional molecular dynamics simulation of particle segregation by shaking. Two different containers are considered: one cylindrical and another with periodic boundary conditions. The dependence of the time evolution of a test particle inside the material is studied as a function of the shaking frequency and amplitude, damping coefficients, and dispersivity.

GRAIN NON-SPHERICITY EFFECTS ON THE ANGLE OF REPOSE OF GRANULAR MATERIAL

We use a site-site model to describe non-sphericity of particles composing a granular media. Specific effects of grain non-sphericity 011 the angle of repose are investigated. We report evidence indicating the possible existence of a shape-roughness threshold for grains: below it angles of repose are essentially the same as those obtained for spherical grains; above it there are pronounced changes 011 the angle of repose and it is possible to find rather large piles of grains.

Accumulation boundaries: codimension-two accumulation of accumulations in phase diagrams of semiconductor lasers, electric circuits, atmospheric and chemical oscillators.

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 boundaries, curves where networks of stable islands of regular oscillations with ever-increasing periodicities accumulate systematically. The experimental exploration of such codimension-two boundaries characterized by the presence of infinite accumulation of accumulations is feasible with existing technology for some of these systems.

Molecular dynamics simulation of powder fluidization in two dimensions

Abstract We report model calculations of a fluidized state in two-dimensional packing of spherical beads subjected to vertical vibrations as recently experimentally studied by Clement and Rajchenbach. Using molecular dynamics we calculate the density field and the velocity distributions of the beads. We discuss the concept of fluidization and propose new ways to characterize it.

Periodicity versus chaos in the dynamics of cobweb models

This paper studies the dynamics of economic models when two parameters are simultaneously varied and concentrates on the dynamics of the cobweb model with adaptive expectations. The simultaneous variation of several parameters intervening in economic processes is a very realistic situation of interest. Using reliable numerical methods, we argue that extended fractal sets in parameter space are relatively common characteristics to be expected for models typically used to describe economic processes. In addition, by choosing appropriate paths in the parameter space, it is possible to observe several different routes to chaos.