Attractor systems and analog computation

Attractor systems are useful in neurodynamics, mainly in the modeling of associative memory. This paper presents a complexity theory for continuous phase space dynamical systems with discrete or continuous time update, which evolve to attractors. In our framework we associate complexity classes with different types of attractors. Fixed points belong to the class BPPd, while chaotic attractors are in NPd. The BPP=NP question of classical complexity theory is translated into a question in the realm of chaotic dynamical systems. This theory enables an algorithmic analysis of attractor networks and flows for the solution of various problem such as linear programming. We exemplify our approach with an analysis of the Hopfield network.