Hernán G. Solari

A Stochastic Spatial Dynamical Model for Aedes Aegypti

We develop a stochastic spatial model for Aedes aegypti populations based on the life cycle of the mosquito and its dispersal. Our validation corresponds to a monitoring study performed in Buenos Aires. Lacking information with regard to the number of breeding sites per block, the corresponding parameter (BS) was adjusted to the data. The model is able to produce numerical data in very good agreement with field results during most of the year, the exception being the fall season. Possible causes of the disagreement are discussed. We analyzed the mosquito dispersal as an advantageous strategy of persistence in the city and simulated the dispersal of females from a source to the surroundings along a 3-year period observing that several processes occur simultaneously: local extinctions, recolonization processes (resulting from flight and the oviposition performed by flyers), and colonization processes resulting from the persistence of eggs during the winter season. In view of this process, we suggest that eradication campaigns in temperate climates should be performed during the winter time for higher efficiency.

Topological analysis of chaotic time series data from the Belousov-Zhabotinskii reaction

SummaryWe have applied topological methods to analyze chaotic time series data from the Belousov-Zhabotinskii reaction. First, the periodic orbits shadowed by the data set were identified. Next, a three-dimensional embedding without self-intersections was constructed from the data set. The topological structure of that flow was visualized by constructing a branched manifold such that every periodic orbit in the flow could be held by the branched manifold. The branched manifold, or induced template, was computed using the three lowest-period orbits. The organization of the higher-period orbits predicted by this induced template was compared with the organization of the orbits reconstructed from the data set with excellent results. The consequences of the presence of certain knots found in the data are discussed.

Stochastic eco-epidemiological model of dengue disease transmission by Aedes aegypti mosquito

We present a stochastic dynamical model for the transmission of dengue that takes into account seasonal and spatial dynamics of the vector Aedes aegypti. It describes disease dynamics triggered by the arrival of infected people in a city. We show that the probability of an epidemic outbreak depends on seasonal variation in temperature and on the availability of breeding sites. We also show that the arrival date of an infected human in a susceptible population dramatically affects the distribution of the final size of epidemics and that early outbreaks have a low probability. However, early outbreaks are likely to produce large epidemics because they have a longer time to evolve before the winter extinction of vectors. Our model could be used to estimate the risk and final size of epidemic outbreaks in regions with seasonal climatic variations.

An efficient algorithm for fast O(N∗ln(N)) box counting

Abstract A new topological ordering is defined which significantly reduces the time requirements for the fast box counting method proposed in a recent paper by Liebovitch and Toth. Only one sorting is necessary in this algorithm.

Sustained oscillations in stochastic systems

Many non-linear deterministic models for interacting populations present damped oscillations towards the corresponding equilibrium values. However, simulations produced with related stochastic models usually present sustained oscillations which preserve the natural frequency of the damped oscillations of the deterministic model but showing non-vanishing amplitudes. The relation between the amplitude of the stochastic oscillations and the values of the equilibrium populations is not intuitive in general but scales with the square root of the populations when the ratio between different populations is kept fixed. In this work, we explain such phenomena for the case of a general epidemic model. We estimate the stochastic fluctuations of the populations around the equilibrium point in the epidemiological model showing their (approximated) relation with the mean values.

Influence of coexisting attractors on the dynamics of a laser system

Abstract We study the interaction among coexisting attractors in a laser model with modulated parameters, and show that these interactions lead to a deterministic truncation of the period doubling bifuraction sequence and to crises of chaotic attractors.

Relative Rotation Rates for Driven Dynamical Systems

Relative rotation rates for two-dimensional driven dynamical systems are defined with respect to arbitrary pairs of periodic orbits. These indices describe the average rate, per period, at which one orbit rotates around another. These quantities are topological invariants of the dynamical system, but contain more physical information than the standard topological invariants for knots, the linking and self-linking numbers„ to which they are closely related. This definition can also be extended to include noisy periodic orbits and strange attractors. A table of the relative rotation rates for a dynamical system, its intertwining matrix, can be used to determine whether orbit pairs can undergo bifurcation and, if so, the order in which the bifurcations can occur. The relative rotation rates are easily computed and measured. They have been computed for a simple model, the laser with modulated parameter. By comparing these indices with those of a zero-torsion lift of a horseshoe return map, we have been able to determine that the dynamics of the laser are governed by the formation of a horseshoe. Additional stable periodic orbits, besides the principal subharmonics previously reported, are predicted by the dynamics. The two additional period-five attractors have been located with the aid of their logical sequence names, and their identification has been confirmed by computing their relative rotation rates.

Laser with injected signal: perturbation of an invariant circle

We study the locked-unloked transition for a class of lasers with injected signal. The transition is produced by a parametric breaking of the invariant circle that represents the free running laser. A Hopf-saddle-node codimension two bifurcation coupled with a phase-drift re-injection mechanism organizes the flow. Fixed points (locked states), periodic orbits and tori, T2, of two inequivalent types as well as hetero-homoclinic loops are found by using methods of bifurcation theory and are illustrated with computer simulations. We discuss the dependence of the flow patterns with respect to the laser parameters and, in particular, we show that the detuning between atomic and cavity frequencies plays a fundamental role for the dynamics.

Semiclassical treatment of spin system by means of coherent states

The semiclassical time‐dependent propagator is studied in terms of the SU(2) coherent states for spin systems. The first‐ and second‐order terms are obtained by means of a detailed calculation. While the first‐order term was established in the earlier days of coherent states the second‐order one is a subject of contradiction. The present approach is developed through a polygonal expansion of the discontinuous paths that enter the path integral. The results here presented are in agreement with only one of the previous approaches, i.e., the one developed on Glauber’s coherent states by means of a direct WKB approximation. It is shown that the present approach gives the exact result in a simple case where it is also possible to observe differences with previous works.

Dengue epidemics and human mobility

In this work we explore the effects of human mobility on the dispersion of a vector borne disease. We combine an already presented stochastic model for dengue with a simple representation of the daily motion of humans on a schematic city of 20 × 20 blocks with 100 inhabitants in each block. The pattern of motion of the individuals is described in terms of complex networks in which links connect different blocks and the link length distribution is in accordance with recent findings on human mobility. It is shown that human mobility can turn out to be the main driving force of the disease dispersal.