Order in Binary Sequences and the Routes to Chaos

The natural order in the space of binary sequences permits to recover the $U$-sequence. Also the scaling laws of the period-doubling cascade and the intermittency route to chaos defined in that ordered set are explained. These arise as intrinsic properties of this ordered set, and independent from any consideration about dynamical systems.Comment: 13 pages, 2 table

Detecting synchronization in spatially extended discrete systems by complexity measurements

The synchronization of two stochastically coupled one-dimensional cellular automata (CA) is analyzed. It is shown that the transition to synchronization is characterized by a dramatic increase of the statistical complexity of the patterns generated by the difference automaton. This singular behavior is verified to be present in several CA rules displaying complex behavior.Comment: 4 pages, 2 figures; you can also visit http://add.unizar.es/public/100_16613/index.htm

Mathematical Biology: Modeling, Analysis, and Simulations

Mathematical biology has been an area of wide interest during the recent decades, as the modeling of complicated biological processes has enabled the creation of analytical and computational approaches to many different bio-inspired problems originating from different branches such as population dynamics, molecular dynamics in cells, neuronal and heart diseases, the cardiovascular system, genetics, etc [...

Complex patterns on the plane: different types of basin fractalization in a two-dimensional mapping

Basins generated by a noninvertible mapping formed by two symmetrically coupled logistic maps are studied when the only parameter \lambda of the system is modified. Complex patterns on the plane are visualised as a consequence of basins' bifurcations. According to the already established nomenclature in the literature, we present the relevant phenomenology organised in different scenarios: fractal islands disaggregation, finite disaggregation, infinitely disconnected basin, infinitely many converging sequences of lakes, countable self-similar disaggregation and sharp fractal boundary. By use of critical curves, we determine the influence of zones with different number of first rank preimages in the mechanisms of basin fractalization.Comment: 19 pages, 11 figure

Statistical Complexity. Applications in Electronic Systems

In this review, a statistical measure of complexity is introduced and its properties are discussed. This measure is based on the interplay between the Shannon information, or a function of it, and the separation of the set of accessible states to a system from the equiprobability distribution, i.e. the disequilibrium. Different applications concerning with quantum systems are shown, from prototypical systems such as the H-atom, to other ones such as the periodic table, the metal clusters, the crystalline bands or the traveling densities. In all of them, this type of statistical indicators shows an interesting behavior able to discern and highlight some conformational properties of those systems

Extremum complexity in the monodimensional ideal gas: the piecewise uniform density distribution approximation

In this work, it is suggested that the extremum complexity distribution of a high dimensional dynamical system can be interpreted as a piecewise uniform distribution in the phase space of its accessible states. When these distributions are expressed as one--particle distribution functions, this leads to piecewise exponential functions. It seems plausible to use these distributions in some systems out of equilibrium, thus greatly simplifying their description. In particular, here we study an isolated ideal monodimensional gas far from equilibrium that presents an energy distribution formed by two non--overlapping Gaussian distribution functions. This is demonstrated by numerical simulations. Also, some previous laboratory experiments with granular systems seem to display this kind of distributions.Comment: 11 pages, 1 table, 16 figure

Statistical complexity, Fisher-Shannon information, and Bohr orbits in the H-atom

The Fisher-Shannon information and a statistical measure of complexity are calculated in the position and momentum spaces for the wave functions of the H-atom. For each level of energy, it is found that these two indicators take their minimum values on the orbitals that correspond to the classical (circular) orbits in the Bohr atomic model, just those with the highest orbital angular momentum.Comment: 7 pages, 2 figure

Long-standing Lymphocutaneous Sporotrichosis

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A method to discern complexity in two-dimensional patterns generated by coupled map lattices

Complex patterns generated by the time evolution of a one-dimensional digitalized coupled map lattice are quantitatively analyzed. A method for discerning complexity among the different patterns is implemented. The quantitative results indicate two zones in parameter space where the dynamics shows the most complex patterns. These zones are located on the two edges of an absorbent region where the system displays spatio-temporal intermittency.Comment: 3 pages, 3 figures; some information about the authors: http://add.unizar.es/public/100_16613/index.htm