Tracking Dynamics of Two-Dimensional Continuous Attractor Neural Networks

Details Tracking Dynamics of Two-Dimensional Continuous Attractor Neural Networks Tracking Dynamics of Two-Dimensional Continuous Attractor Neural Networks

2009-10-08

arxiv.org/abs/0910.1520v1

J. Phys.: Conf. Ser. (2009) 197: 012017

Physics

Condensed Matter

Disordered Systems and Neural Networks

10 pages and 10 figures

Scientific paper

10.1088/1742-6596/197/1/012017

We introduce an analytically solvable model of two-dimensional continuous attractor neural networks (CANNs). The synaptic input and the neuronal response form Gaussian bumps in the absence of external stimuli, and enable the network to track external stimuli by its translational displacement in the two-dimensional space. Basis functions of the two-dimensional quantum harmonic oscillator in polar coordinates are introduced to describe the distortion modes of the Gaussian bump. The perturbative method is applied to analyze its dynamics. Testing the method by considering the network behavior when the external stimulus abruptly changes its position, we obtain results of the reaction time and the amplitudes of various distortion modes, with excellent agreement with simulation results.

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