Symbolic dynamics generated by a hybrid chaotic systems

We consider piecewise defined differential dynamical systems which can be analysed through symbolic dynamics and transition matrices. We have a continuous regime, where the time flow is characterized by an ordinary differential equation (ODE) which has explicit solutions, and the singular regime, where the time flow is characterized by an appropriate transformation. The symbolic codification is given through the association of a symbol for each distinct regular system and singular system. The transition matrices are then determined as linear approximations to the symbolic dynamics. We analyse the dependence on initial conditions, parameter variation and the occurrence of global strange attractors.

José Rodrigues Santos de Sousa Ramos (1948-2007): The diversity of dynamical systems

José Rodrigues Santos de Sousa Ramos, mathematician of great merit, passed away on January 1st, 2007, in Lisbon. He was buried in Sobral da Adiça. His death was a huge loss for the development of mathematics in Portugal. The course of time will increase the dimension of this loss. Therefore, we dedicated this theme issue on Dynamical Systems to recall his memory and underline his work. We never forget you.

Central Algarve karst system tufa-related dynamics, Portugal.

Geomorphological mapping is a powerful instrument improving the geomorphological interpretation and understanding of the processes and forms used in landscape studies, with the ability of organizing different thematic layers in the same map. The presented map provide relevant information about the different geomorphological units of the central Algarve (i.e. the Carboniferous flysch mountains; the Barrocal, with marly and karstified subunits), where a karst system is prominent. Solution karst morphologies and large dry areas are common in the elevated areas of the Barrocal, suggesting deep circulation of groundwater. These recharge areas feed the perched aquifers of the area, where discharge is controlled by the impervious lithologies (clay-rich strata of the turbidites, marls and argilites) in the valley bottoms or other leaks in dammed aquifers. In springs related to the main aquifers tufa are actively being formed and, close coupled to spring location, different tufa depositional systems develop.

Effect of trees in the soil nutrient concentration and pasture produtivity in Mediterranean silvo-pastoral systems

Silvo-pastoral are mixed systems of trees and grass, which have been proposed as a means to extend the benefits of forest to farmed land. Agro-forestry systems under semi-arid Mediterranean conditions, called montados in Portugal and dehesas in Spain, cover substantial areas in the world. These silvo-pastoral systems are the most extensive European agro-forestry system, as they cover 3.5–4.0 Mha in Spain and Portugal. Long-term studies are essential to assess the magnitude of the temporal nutrient flow dynamics in terrestrial ecosystems and to understand the response of these systems to fertilizer management. In order to implement the conservation task and recovery of resources through silvo-pastoral systems it is necessary to know and correct potential limiting factors, especially the soil factor, and this requires agronomic knowledge as well as the implmentation of the available new technologies. In this context, this task aims at a better understanding of the contribution of the two components of montado ecosystem (trees and herbaceous vegetation) on the soil nutrient and water dynamics, that allow for the interpretation of the variability of pasture dry matter yield and help the farmer in the management of tree density. Collaterally the task will evaluate and calibrate new technologies that simplify the monitoring of soil, grassland, trees and grazing animals.

Federative dynamics in the EU under the influence of EU citizenship rights in times of crisis

The federative debate has been tied to the history of the EU integration from the start. Even though the EU is a polity in formation, the comparison with the state model has limited usefulness in assessing the evolution of federative dynamics in the EU. In the context of the EU, federalism should not be regarded as a static arrangement, but rather as a process that has been unfolding despite or because of EU integration setbacks. By the same token, EU citizenship is necessarily distinct from national citizenship. Our purpose in this article is to understand the federative dynamics of the EU in relation to the emergence of a “community of rights”. We also aim to establish if, and how, the on-going crisis has triggered a change in the EU federative process as a result of the weakening/strengthening of citizenship rights.

An R package for simulating metapopulation dynamics and range expansion under environmental change

The metapopulation paradigm is central in ecology and conservation biology to understand the dynamics of spatially-structured populations in fragmented landscapes. Metapopulations are often studied using simulation modelling, and there is an increasing demand of user-friendly software tools to simulate metapopulation responses to environmental change. Here we describe the MetaLandSim R package, mwhich integrates ideas from metapopulation and graph theories to simulate the dynamics of real and virtual metapopulations. The package offers tools to (i) estimate metapopulation parameters from empirical data, (ii) to predict variation in patch occupancy over time in static and dynamic landscapes, either real or virtual, and (iii) to quantify the patterns and speed of metapopulation expansion into empty landscapes. MetaLandSim thus provides detailed information on metapopulation processes, which can be easily combined with land use and climate change scenarios to predict metapopulation dynamics and range expansion for a variety of taxa and ecological systems.