Self organization and evolution in mathematical models

Abstract
Through several examples we illustrate to non mathematicians how biological situations can be translated in mathematical terms. Even simple mathematical models can be very efficient to clarify a complex biological situation and the same basic mathematical procedures can be found in different biological frameworks. In particular stability analysis under small fluctuations of non linear models possessing different time scales is fundamental, especially bifurcation properties. An important issue is also to choose between deterministic and stochastic models. We illustrate these points through classical examples coming from the formation of patterns (morphogenesis), vision (visual hallucinations), onset of periodic oscillations in the neuronal activity due to random noise and a mathematically related example of stochastic resonance.