Dynamics of Neural Networks with Continuous Attractors

Abstract

We investigate the dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of their neuronal interactions, CANNs can hold a continuous family of stationary states. We systematically explore how their neutral stability facilitates the tracking performance of a CANN, which is believed to have wide applications in brain functions. We develop a perturbative approach that utilizes the dominant movement of the network stationary states in the state space. We quantify the distortions of the bump shape during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable, and the reaction time to catch up an abrupt change in stimulus.

6 pages, 7 figures with 4 captions

References in corpus (1)

• Geometry of density sates

Cited by in corpus (4)

• A Moving Bump in a Continuous Manifold: A Comprehensive Study of the Tracking Dynamics of Continuous Attractor Neural Networks
• Tracking Dynamics of Two-Dimensional Continuous Attractor Neural Networks
• Bimodular continuous attractor neural networks with static and moving stimuli
• Discrete-attractor-like Tracking in Continuous Attractor Neural Networks