Strong and weak Allee effects and chaotic dynamics in Richards' growths

In this paper we define and investigate generalized Richards' growth models with strong and weak Allee effects and no Allee effect. We prove the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, depending on the implicit conditions, which involve the several parameters considered in the models. New classes of functions describing the existence or not of Allee effect are introduced, a new dynamical approach to Richards' populational growth equation is established. These families of generalized Richards' functions are proportional to the right hand side of the generalized Richards' growth models proposed. Subclasses of strong and weak Allee functions and functions with no Allee effect are characterized. The study of their bifurcation structure is presented in detail, this analysis is done based on the configurations of bifurcation curves and symbolic dynamics techniques. Generically, the dynamics of these functions are classified in the following types: extinction, semi-stability, stability, period doubling, chaos, chaotic semistability and essential extinction. We obtain conditions on the parameter plane for the existence of a weak Allee effect region related to the appearance of cusp points. To support our results, we present fold and flip bifurcations curves and numerical simulations of several bifurcation diagrams.

A cellulosic liquid crystal pool for cellulose nanocrystals: structure and molecular dynamics at high shear rates

Cellulose and its derivatives, such as hydroxypropylcellulose (HPC) have been studied for a long time but they are still not well understood particularly in liquid crystalline solutions. These systems can be at the origin of networks with properties similar to liquid crystalline (LC) elastomers. The films produced from LC solutions can be manipulated by the action of moisture allowing for instance the development of a soft motor (Geng et al., 2013) driven by humidity. Cellulose nanocrystals (CNC), which combine cellulose properties with the specific characteristics of nanoscale materials, have been mainly studied for their potential as a reinforcing agent. Suspensions of CNC can also self-order originating a liquid-crystalline chiral nematic phases. Considering the liquid crystalline features that both LC-HPC and CNC can acquire, we prepared LC-HPC/CNC solutions with different CNC contents (1,2 and 5 wt.%). The effect of the CNC into the LC-HPC matrix was determined by coupling rheology and NMR spectroscopy - Rheo-NMR a technique tailored to analyse orientational order in sheared systems. (C) 2015 Elsevier Ltd. All rights reserved.

Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models

In this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet's functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of this class of functions in a neighborhood of a bifurcation point PBB, in a two-dimensional parameter space, there exists an order regarding how the infinite number of periodic orbits are born: the Sharkovsky ordering. Consequently, the corresponding symbolic sequences follow the usual unimodal kneading sequences in the topological ordered tree. We verified that under some sufficient conditions, Weibull-Gompertz-Fréchet's functions have a particular bifurcation structure: a big bang bifurcation point PBB. This fractal bifurcations structure is of the so-called "box-within-a-box" type, associated to a boxe ω1, where an infinite number of bifurcation curves issues from. This analysis is done making use of fold and flip bifurcation curves and symbolic dynamics techniques. The present paper is an original contribution in the framework of the big bang bifurcation analysis for continuous maps.

Mapping freshwater snails in Angola: distribution, identity and molecular diversity of medically important taxa

Introduction - This study was designed to determine the presence and identity of potential intermediate snail hosts of schistosomiasis in Bengo, Luanda, Kwanza Norte and Malanje Provinces in NW Angola. This is an area where infection with Schistosoma haematobium, causing urogenital schistosomiasis, is common but little is known about transmission of the disease. Angola has had a varied past with regards to disease control and is revitalising efforts to combat Neglected Tropical Diseases.

Measuring and Controlling the Chaotic Motion of Profits

The study of economic systems has generated deep interest in exploring the complexity of chaotic motions in economy. Due to important developments in nonlinear dynamics, the last two decades have witnessed strong revival of interest in nonlinear endogenous business chaotic models. The inability to predict the behavior of dynamical systems in the presence of chaos suggests the application of chaos control methods, when we are more interested in obtaining regular behavior. In the present article, we study a specific economic model from the literature. More precisely, a system of three ordinary differential equations gather the variables of profits, reinvestments and financial flow of borrowings in the structure of a firm. Firstly, using results of symbolic dynamics, we characterize the topological entropy and the parameter space ordering of kneading sequences, associated with one-dimensional maps that reproduce significant aspects of the model dynamics. The analysis of the variation of this numerical invariant, in some realistic system parameter region, allows us to quantify and to distinguish different chaotic regimes. Finally, we show that complicated behavior arising from the chaotic firm model can be controlled without changing its original properties and the dynamics can be turned into the desired attracting time periodic motion (a stable steady state or into a regular cycle). The orbit stabilization is illustrated by the application of a feedback control technique initially developed by Romeiras et al. [1992]. This work provides another illustration of how our understanding of economic models can be enhanced by the theoretical and numerical investigation of nonlinear dynamical systems modeled by ordinary differential equations.

O teatro na comunidade de Torres Vedras: as práticas de criação e de fruição em torno do grupo do Grémio Artístico Torreense

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Educação Artística - Especialização em Teatro na Educação

Performance comparison of a VDFLL versus VDLL and scalar GNSS receiver architectures in Harsh scenarios

We analyze the advantages and drawbacks of a vector delay/frequency-locked loop (VDFLL) architecture regarding the conventional scalar and the vector delay-locked loop (VDLL) architectures for GNSS receivers in harsh scenarios that include ionospheric scintillation, multipath, and high dynamics motion. The VDFLL is constituted by a bank of code and frequency discriminators feeding a central extended Kaiman filter (EKF) that estimates the receiver's position, velocity, and clock bias. Both code and frequency loops are closed vectorially through the EKF. The VDLL closes the code loop vectorially and the phase loops through individual PLLs while the scalar receiver closes both loops by means of individual independent PLLs and DLLs.

Molecular mobility, composition and structure analysis in glycerol plasticised chitosan films

This study was developed with the purpose to investigate the effect of polysaccharide/plasticiser concentration on the microstructure and molecular dynamics of polymeric film systems, using transmission electron microscope imaging (TEM) and nuclear magnetic resonance (NMR) techniques. Experiments were carried out in chitosan/glycerol films prepared with solutions of different composition. The films obtained after drying and equilibration were characterised in terms of composition, thickness and water activity. Results show that glycerol quantities used in film forming solutions were responsible for films composition; while polymer/total plasticiser ratio in the solution determined the thickness (and thus structure) of the films. These results were confirmed by TEM. NMR allowed understanding the films molecular rearrangement. Two different behaviours for the two components analysed, water and glycerol were observed: the first is predominantly moving free in the matrix, while glycerol is mainly bounded to the chitosan chain. (C) 2013 Elsevier Ltd. All rights reserved.