Volume 84, Number 1, October 2008
Article Number 18002
Number of page(s) 6
Section Interdisciplinary Physics and Related Areas of Science and Technology
Published online 18 September 2008
EPL, 84 (2008) 18002
DOI: 10.1209/0295-5075/84/18002

Dynamics of neural networks with continuous attractors

C. C. Alan Fung1, K. Y. Michael Wong1 and Si Wu2

1   Department of Physics, Hong Kong University of Science and Technology - Clear Water Bay, Hong Kong, China
2   Department of Informatics, University of Sussex - Brighton, UK, EU

received 19 May 2008; accepted in final form 22 August 2008; published October 2008
published online 18 September 2008

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.

87.10.-e - Biological and medical physics: General theory and mathematical aspects.
05.45.-a - Nonlinear dynamics and chaos.

© EPLA 2008