Analysis of Dynamical Systems using Predicate Transformers: Attraction and Composition

. We present a framework for the compositional analysis of dynamical systems. This framework is based on set-valued functions, defined by predicate transformers. It integrates concepts from mathematics, computing science, and neurosciences. We also introduce an additional concept: the attraction between predicates. The main results of the paper are then presented. We propose composition rules which permit to see a complex system as composed of simpler ones, to study these simple systems using the concepts introduced before, and then to compose the results for deriving the analysis of the initial complex system. 1 Introduction Discrete autonomous dynamical systems [1, 2] can be analyzed using predicate transformers for iterated guarded commands [3]. Initial results of such a study have been reported [4]; they provide sufficient criteria on invariants of infinite iterations for detecting topological transitivity and sensitive dependence on initial conditions. The present paper tackles t..