Phase transitions induced by diversity and examples in biological systems

PhD thesis public defence. Supervisor: Raúl Toral.

The thesis covers different aspects of scientific research. On one end there is an analysis of a specific model for intestinal absorption. A good theoretical understanding of the mathematics can be a guide to the experimentalist and help estimate the fitting of the model parameters to the measurements. On the other end there are abstract models whose relation to specific physical or biological systems seems far but the conclusions drawn from them tend to be quite general. We analyse \'magnetic\' systems with diverse parameters that show transitions between disordered and ordered states. Within both ends of the scientific spectrum we investigate a system of coupled biochemical oscillators resembling a simplified version of the circadian pacemaker neurons and a more abstract oscillatory (excitable) system called \"active rotators\". We are interested in the effects of diversity in the parameters on the collective motion of the oscillators.