This coordinated project is part of a long-term programme of research that has been carried out by these the two teams during at least the past two decades. The program aims to understand the fundamental dynamical aspects of living systems as well as the development of prebiotic inorganic structures relevant to life by means of the application of dynamical systems techniques. The cases under study for which continued financing we request with this grant application include the structure of the genetic code, functioning of the auditory system, the formation of nacre -closely related to the the evolution of chemical gardens, left-right symmetry breaking during the development of embryos, the individual and colonial motion of swimming of microorgnaisms, the dynamical description of cell division at different scales and instances, etc. These have been chosen as representative and interesting examples for our approach of applying dynamical-systems methods to biology for two reasons: on one hand, each of these cases is of intrinsic and relevant interest in different biological fields; and, on the other, they compose a more general whole that moves us forward towards our long-term goal of contributing to the mathematization of biology through the application of ideas from dynamical systems.

Central to our approach is to make essential use of the development of a modeling technique based on qualitative dynamics but aiming to produce very well defined quantitative predictions from the fundamental hypothesis. Some of these dynamical-systems techniques and methods must be concurrently developed alongside the biological investigations as it was the case of the development of a proper theory for three-frequency dynamical systems when we have applied it to perceptive phenomena in the auditory system. Therefore, the marriage of dynamics and biology drives forward not only the application field but also the parent field of dynamical systems itself. With this in mind, the proposal is to distribute our efforts in a balanced way between the development of the apropriated mathematical and physical tools and the research and the aplication to the specific problems.