First-order resonances in three-degrees-of-freedom systems

Hamiltonian systems with three degrees of freedom which have a resonance-ratio 1∶2∶ω with ω=1, 2, 3, or 4 are studied here. The periodic orbits are determined together with their stability characteristics. Furthermore we shall study the fundamental question of asymptotic integrability of these systems.     

Habitat suitability modelling as a mapping tool for macrobenthic communities: An example from the Belgian part of the North Sea

Being ecologically important and well-known, the spatial distribution pattern of the macrobenthos is often used to support an ecologically sustainable marine management. Though in many cases the macrobenthic spatial distribution is relatively well-known, this information is merely restricted to point observations at the sampling stations: although being increasingly demanded, full coverage spatial distribution maps are generally lacking. This study therefore aimed at demonstrating the usefulness of habitat suitability modelling as a full coverage mapping tool with high relevance for marine management through (1) the construction of a habitat suitability model for the soft sediment macrobenthic communities in the Belgian part of the North Sea (BPNS) and (2) predicting the full coverage spatial distribution of macrobenthic communities within the BPNS. The BPNS was selected as a case study area because of the high data availability on both macrobenthos and environmental characteristics. Discriminant function analysis (DFA) objectively selected median grain size and sediment mud content and omitted bathymetry, slope and distance to the coast to represent the most important environmental variables determining the macrobenthic community distribution. The consequent crossvalidated, empirical habitat suitability model, using both median grain size and mud content, showed an a posteriori average correctly classified instances (CCI) of 79% (community-dependent CCI ranging from 72% to 86%) and a Cohen's kappa of 0.71, pointing towards a very good agreement between model predictions and observations. The application of the habitat suitability model on the full coverage maps of median grain size and sediment mud content, taken from literature, allowed to reliably assess the distribution of the macrobenthic communities within 96.3% of the 53,297 BPNS grid cells with a resolution of 250 m. Next to its applicability to the BPNS, the model is further anticipated to potentially perform well in the full Southern Bight of the North Sea: testing is advised here. Since the habitat suitability is considered far more stable through time compared to the permanently fluctuating macrobenthic communities, information on the habitat suitability of an area is considered highly important for a scientifically sound marine management.