Transients of active tracking: A stroll in attractor spaces

Abstract

We present the dynamical analysis of embodied RNNs evolved to control a cybernetic device that solves a tracking problem. From the Neurodynamics perspective, we analyze the networks with focus on a characterization of the attractors and attractor sequences, guiding the transients. Projections of these attractors to motor space help visualizing the shape of the attractors, thus pointing to the underpinnings of behavior. Among the different attractors found are fixed points, periodic and quasi-periodic attractors of different periods, as well as chaos. Further analysis of the attractors relates changes of shape, size and period to motor control. Interesting characteristic behaviors arise, such as chaotic transitory regimes and implicit mapping of environmental assymmetricities in the network's response, (as for example attractor hops that implicitly code for gravity). We discuss autonomy, capacity and some issues relating to a possible theory of transients. © Springer-Verlag Berlin Heidelberg 2007.