Attractor network

An attractor network is a type of recurrent dynamical network, that evolves toward a stable pattern over time. Nodes in the attractor network converge toward a pattern that may either be fixed-point (a single state), cyclic (with regularly recurring states), chaotic (locally but not globally unstable) or random (stochastic). Attractor networks have largely been used in computational neuroscience to model neuronal processes such as associative memory and motor behavior, as well as in biologically inspired methods of machine learning. An attractor network contains a set of n nodes, which can be represented as vectors in a d-dimensional space where n>d. Over time, the network state tends toward one of a set of predefined states on a d-manifold; these are the attractors. Attractor In attractor networks, an attractor (or attracting set) is a closed subset of states A toward which the system of nodes evolves. A stationary attractor is a state or sets of states where the global dynamics of the network stabilize. Cyclic attractors evolve the network toward a set of states in a limit cycle, which is repeatedly traversed. Chaotic attractors are non-repeating bounded attractors that are continuously traversed. The network state space is the set of all possible node states. The attractor space is the set of nodes on the attractor. Attractor networks are initialized based on the input pattern. The dimensionality of the input pattern may differ from the dimensionality of the network nodes. The trajectory of the network consists of the set of states along the evolution path as the network converges toward the attractor state. The basin of attraction is the set of states that results in movement towards a certain attractor. Various types of attractors may be used to model different types of network dynamics. While fixed-point attractor networks are the most common (originating from Hopfield networks), other types of networks are also examined. The fixed point attractor naturally follows from the Hopfield network.