Big Bang bifurcations and allee effect in Blumberg’s dynamics

This paper concerns dynamics and bifurcations properties of a class of continuous-defined one-dimensional maps, in a three-dimensional parameter space: Blumberg's functions. This family of functions naturally incorporates a major focus of ecological research: the Allee effect. We provide a necessary condition for the occurrence of this phenomenon, associated with the stability of a fixed point. A central point of our investigation is the study of bifurcations structure for this class of functions. We verified that under some sufficient conditions, Blumberg's functions have a particular bifurcations structure: the big bang bifurcations of the so-called "box-within-a-box" type, but for different kinds of boxes. Moreover, it is verified that these bifurcation cascades converge to different big bang bifurcation curves, where for the corresponding parameter values are associated distinct attractors. This work contributes to clarify the big bang bifurcation analysis for continuous maps. To support our results, we present fold and flip bifurcations curves and surfaces, and numerical simulations of several bifurcation diagrams.

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.

Explosion birth and extinction: Double big bang bifurcations and Allee effect in Tsoularis-Wallace's growth models

This work concerns dynamics and bifurcations properties of a new class of continuous-defined one-dimensional maps: Tsoularis-Wallace's functions. This family of functions naturally incorporates a major focus of ecological research: the Allee effect. We provide a necessary condition for the occurrence of this phenomenon of extinction. To establish this result we introduce the notions of Allee's functions, Allee's effect region and Allee's bifurcation curve. Another central point of our investigation is the study of bifurcation structures for this class of functions, in a three-dimensional parameter space. We verified that under some sufficient conditions, Tsoularis-Wallace's functions have particular bifurcation structures: the big bang and the double big bang bifurcations of the so-called "box-within-a-box" type. The double big bang bifurcations are related to the existence of flip codimension-2 points. Moreover, it is verified that these bifurcation cascades converge to different big bang bifurcation curves, where for the corresponding parameter values are associated distinct kinds of boxes. This work contributes to clarify the big bang bifurcation analysis for continuous maps and understand their relationship with explosion birth and extinction phenomena.

Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects

The main purpose of this work was to study population dynamic discrete models in which the growth of the population is described by generalized von Bertalanffy's functions, with an adjustment or correction factor of polynomial type. The consideration of this correction factor is made with the aim to introduce the Allee effect. To the class of generalized von Bertalanffy's functions is identified and characterized subclasses of strong and weak Allee's functions and functions with no Allee effect. This classification is founded on the concepts of strong and weak Allee's effects to population growth rates associated. A complete description of the dynamic behavior is given, where we provide necessary conditions for the occurrence of unconditional and essential extinction types. The bifurcation structures of the parameter plane are analyzed regarding the evolution of the Allee limit with the aim to understand how the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, is realized. To generalized von Bertalanffy's functions with strong and weak Allee effects is identified an Allee's effect region, to which is associated the concepts of chaotic semistability curve and Allee's bifurcation point. We verified that under some sufficient conditions, generalized von Bertalanffy's functions have a particular bifurcation structure: the big bang bifurcations of the so-called box-within-a-box type. To this family of maps, the Allee bifurcation points and the big bang bifurcation points are characterized by the symmetric of Allee's limit and by a null intrinsic growth rate. The present paper is also a significant contribution in the framework of the big bang bifurcation analysis for continuous 1D maps and unveil their relationship with the explosion birth and the extinction phenomena.

Microcosmos no cinema português contemporâneo: um mundo pós – Big Brother

O projecto “Principais tendências no cinema português contemporâneo” nasceu no Departamento de Cinema da ESTC, com o objectivo de desenvolver investigação especializada a partir de um núcleo formado por alunos da Licenciatura em Cinema e do Mestrado em Desenvolvimento de Projecto Cinematográfico, a que se juntaram professores-investigadores membros do CIAC e convidados. O que agora se divulga corresponde a dois anos e meio de trabalho desenvolvido pela equipa de investigação, entre Abril de 2009 e Novembro de 2011. Dada a forma que ele foi adquirindo, preferimos renomeá-lo, para efeitos de divulgação, “Novas & velhas tendências no cinema português contemporâneo”.

Convective patterns under the Indo-Atlantic << box >>

Using fluid mechanics, we reinterpret the mantle images obtained from global and regional tomography together with geochemical, geological and paleomagnetic observations, and attempt to unravel the pattern of convection in the Indo-Atlantic "box" and its temporal evolution over the last 260 Myr. The << box >> presently contains a) a broad slow seismic anomaly at the CMB which has a shape similar to Pangea 250 Myr ago, and which divides into several branches higher in the lower mantle, b) a "superswell, centered on the western edge of South Africa, c) at least 6 "primary hotspots" with long tracks related to traps, and d) numerous smaller hotspots. In the last 260 Myr, this mantle box has undergone 10 trap events, 7 of them related to continental breakup. Several of these past events are spatially correlated with present-day seismic anomalies and/or upwellings. Laboratory experiments show that superswells, long-lived hotspot tracks and traps may represent three evolutionary stages of the same phenomenon, i.e. episodic destabilization of a hot, chemically heterogeneous thermal boundary layer, close to the bottom of the mantle. When scaled to the Earth's mantle, its recurrence time is on the order of 100-200 Myr. At any given time, the Indo-Atlantic box should contain 3 to 9 of these instabilities at different stages of their development, in agreement with observations. The return flow of the downwelling slabs, although confined to two main << boxes >> (Indo-Atlantic and Pacific) by subduction zone geometry, may therefore not be passive, but rather take the form of active thermochemical instabilities. (c) 2005 Elsevier B.V. All rights reserved.