Continuous attractor is a promising model for describing the encoding of continuous stimuli in neural systems. In a continuous attractor, the stationary states of the neural system form a continuous parameter space, on which the system is neutrally stable. This property enables the neutral system to track time-varying stimulus smoothly. In this study we investigate the tracking speed of continuous attractors. In order to analyze the dynamics of a large-size network, which is otherwise extremely complicated, we develop a strategy to reduce its dimensionality by utilizing the fact that a continuous attractor can eliminate the input components perpendicular to the attractor space very quickly. We therefore project the network dynamics onto the tangent of the attractor space, and simplify it to be a one-dimension Ornstein-Uhlenbeck process. With this approximation we elucidate that the reaction time of a continuous attractor increases logarithmically with the size of the stimulus change. This finding may have important implication on the mental rotation behavior. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Wu, S., Hamaguchi, K., & Amari, S. I. (2007). The tracking speed of continuous attractors. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4491 LNCS, pp. 926–934). Springer Verlag. https://doi.org/10.1007/978-3-540-72383-7_108
Mendeley helps you to discover research relevant for your work.