Deterministic and stochastic dynamics of models from Neuroscience, Epidemiology, Biology and other branches of the Applied Sciences

PI (U. Sevilla): Tomás Caraballo Garrido

co-PI (U. Sevilla): José Antonio Langa Rosado

Abstract: The main aims of this project can be classified into two main groups. On the one hand, we will continue investigating and developing the challenging issues which still have to be undertaken in the theoretical aspects of the fields of non-autonomous and stochastic dynamical systems, especially on the asymptotic behaviour of dynamical systems (deterministic and stochastic) by analyzing the existence and geometrical structure of their attracting and invariant sets/manifolds, some bifurcation scenarios, etc,  taking into account the possibility that the problems can exhibit some additional feature (can contain delay or memory in their formulations–very likely to happen in many real situations; may not have uniqueness of solutions, possessing random or stochastic terms; experiencing some sudden jumps or impulses on the behaviour, etc). 

On the other hand, we will tackle more risky and challenging research directions. More precisely, we plan to go deeper and further in the development of the current applied research directions that we are considering now, and to initiate some new lines of investigation which can be very useful and helpful in some interesting and important problems from Neuroscience, Epidemiology, Biology and some other branches from the applied sciences.