Complete synchronization and delayed synchronization in couplings

We consider a general coupling of two identical chaotic dynamical systems, and we obtain the conditions for synchronization. We consider two types of synchronization: complete synchronization and delayed synchronization. Then, we consider four different couplings having different behaviors regarding their ability to synchronize either completely or with delay: Symmetric Linear Coupled System, Commanded Linear Coupled System, Commanded Coupled System with delay and symmetric coupled system with delay. The values of the coupling strength for which a coupling synchronizes define its Window of synchronization. We obtain analytically the Windows of complete synchronization, and we apply it for the considered couplings that admit complete synchronization. We also obtain analytically the Window of chaotic delayed synchronization for the only considered coupling that admits a chaotic delayed synchronization, the commanded coupled system with delay. At last, we use four different free chaotic dynamics (based in tent map, logistic map, three-piecewise linear map and cubic-like map) in order to observe numerically the analytically predicted windows.

How Complex, Probable, and Predictable is Genetically Driven Red Queen Chaos?

Coevolution between two antagonistic species has been widely studied theoretically for both ecologically- and genetically-driven Red Queen dynamics. A typical outcome of these systems is an oscillatory behavior causing an endless series of one species adaptation and others counter-adaptation. More recently, a mathematical model combining a three-species food chain system with an adaptive dynamics approach revealed genetically driven chaotic Red Queen coevolution. In the present article, we analyze this mathematical model mainly focusing on the impact of species rates of evolution (mutation rates) in the dynamics. Firstly, we analytically proof the boundedness of the trajectories of the chaotic attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. By using symbolic dynamics theory, we quantify the complexity of genetically driven Red Queen chaos computing the topological entropy of existing one-dimensional iterated maps using Markov partitions. Co-dimensional two bifurcation diagrams are also built from the period ordering of the orbits of the maps. Then, we study the predictability of the Red Queen chaos, found in narrow regions of mutation rates. To extend the previous analyses, we also computed the likeliness of finding chaos in a given region of the parameter space varying other model parameters simultaneously. Such analyses allowed us to compute a mean predictability measure for the system in the explored region of the parameter space. We found that genetically driven Red Queen chaos, although being restricted to small regions of the analyzed parameter space, might be highly unpredictable.

Simulation of wave action on a moored container carrier inside Sines’ Harbour

The integrated numerical tool SWAMS (Simulation of Wave Action on Moored Ships) is used to simulate the behavior of a moored container carrier inside Sines’ Harbour. Wave, wind, currents, floating ship and moorings interaction is discussed. Several case scenarios are compared differing in the layout of the harbour and wind and wave conditions. The several harbour layouts correspond to proposed alternatives for the future expansion of Sines’ terminal XXI that include the extension of the East breakwater and of the quay. Additionally, the influence of wind on the behavior of the ship moored and the introduction of pre tensioning the mooring lines was analyzed. Hydrodynamic forces acting on the ship are determined using a modified version of the WAMIT model. This modified model utilizes the Haskind relations and the non-linear wave field inside the harbour obtained with finite element numerical model, BOUSS-WMH (Boussinesq Wave Model for Harbors) to get the wave forces on the ship. The time series of the moored ship motions and forces on moorings are obtained using BAS solver. © 2015 Taylor & Francis Group, London.