Model transform and local parameters. Application to instantaneous attractors

Abstract

The model transform fits exactly the parameters of a suitable model to empirical or simulated data in each point in time and/or space. We describe several examples of concrete model transforms and their applications. The model transform allows simple theoretical models to be applied to complex empirical systems in each short interval of time or/and in each local neighborhood. The model can be chosen to identify, for instance, the temporal evolution of the attractor landscape for empirical systems which depict a complex dynamics over time.