Topological Complexity and Predictability in the Dynamics of a Tumor Growth Model with Shilnikov's Chaos

Dynamical systems modeling tumor growth have been investigated to determine the dynamics between tumor and healthy cells. Recent theoretical investigations indicate that these interactions may lead to different dynamical outcomes, in particular to homoclinic chaos. In the present study, we analyze both topological and dynamical properties of a recently characterized chaotic attractor governing the dynamics of tumor cells interacting with healthy tissue cells and effector cells of the immune system. By using the theory of symbolic dynamics, we first characterize the topological entropy and the parameter space ordering of kneading sequences from one-dimensional iterated maps identified in the dynamics, focusing on the effects of inactivation interactions between both effector and tumor cells. The previous analyses are complemented with the computation of the spectrum of Lyapunov exponents, the fractal dimension and the predictability of the chaotic attractors. Our results show that the inactivation rate of effector cells by the tumor cells has an important effect on the dynamics of the system. The increase of effector cells inactivation involves an inverse Feigenbaum (i.e. period-halving bifurcation) scenario, which results in the stabilization of the dynamics and in an increase of dynamics predictability. Our analyses also reveal that, at low inactivation rates of effector cells, tumor cells undergo strong, chaotic fluctuations, with the dynamics being highly unpredictable. Our findings are discussed in the context of tumor cells potential viability.

Modelo SIG para apoio à análise de sistemas de transportes e usos do solo

Dissertação de natureza científica para obtenção do grau de Mestre em Engenharia Civil

Technical and economic assessment of energy from Tidal Currents

The present work aims to study the feasibility of deploying a farm of sea current turbines for electricity generation in Portugal. An approach to the tides, which are they, how they are formed, its prediction, is held. It is also conducted a study about the energy of sea currents and it is presented some technology about ocean currents too. A model of tidal height and velocity of the currents it is also developed. The energy produced by a hypothetical park, built in Sines (Portugal), is calculated and afterwards, an economical assessment is performed for two possible scenarios and a sensitivity analysis of NVP (Net Present Value) and LCOE (Levelized Cost of Energy) is figured. The conclusions about the feasibility of the projects are also presented. Despite being desired due to its predictability, this energy source is not yet economically viable as it is in an initial state of development. To push investment in this technology a feed-in tariff of, at least €200/MWh, should be considered.

Technical and economic assessment of energy from Tidal Currents

The present work aims to study the feasibility of deploying a farm of sea current turbines for electricity generation in Portugal. An approach to the tides, which are they, how they are formed, its prediction, is held. It is also conducted a study about the energy of sea currents and it is presented some technology about ocean currents too. A model of tidal height and velocity of the currents it is also developed. The energy produced by a hypothetical park, built in Sines (Portugal), is calculated and afterwards, an economical assessment is performed for two possible scenarios and a sensitivity analysis of NVP (Net Present Value) and LCOE (Levelized Cost of Energy) is figured. The conclusions about the feasibility of the projects are also presented. Despite being desired due to its predictability, this energy source is not yet economically viable as it is in an initial state of development. To push investment in this technology a feed-in tariff of, at least €200/MWh, should be considered.

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.