Network attractors and nonlinear dynamics of neural computation

Abstract

The importance of understanding the nonlinear dynamics of neural systems, and the relation to cognitive systems more generally, has been recognized for a long time. Approaches that analyse neural systems in terms of attractors of autonomous networks can be successful in explaining system behaviours in the input-free case. Nonetheless, a computational system usually needs inputs from its environment to effectively solve problems, and this necessitates a non-autonomous framework where typically the effects of a changing environment can be studied. In this review we highlight a variety of network attractors that can exist in autonomous systems and can be used to aid interpretation of the dynamics in the presence of inputs. Such network attractors (that consist of heteroclinic or excitable connections between invariant sets) lend themselves to modelling discretestate computations with continuous inputs, and can sometimes be thought of as a hybrid model between classical discrete computation and continuous-time dynamical systems.