The Tracking Speed of Continuous Attractors

  • Si Wu
  • Kosuke Hamaguchi
  • Shun-ichi Amari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4491)


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.


Network Dynamic Neural System Mental Rotation External Input Neutral Stability 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Si Wu
    • 1
  • Kosuke Hamaguchi
    • 2
  • Shun-ichi Amari
    • 2
  1. 1.Department of Informatics, University of SussexUK
  2. 2.Amari Research Unit, RIKEN Brain Science InstituteJapan

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