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Continuous Attractor Network Model for Conjunctive Position-by-Velocity Tuning of Grid Cells

Figure 5

The network performs robust path-integration against perturbations in weights (parameters: ).

(A–F) Perturbation by Gaussian random noise with zero mean and standard deviation 2% or 10% relative to the weight range. A,C: Scatter plots of the velocity of the bumps with respect to the velocity of the virtual animal for 2% perturbation (A) or 10% perturbation (C). Every 100 ms in the simulation, the instantaneous velocities of the bumps and the animal during 1 ms interval is marked by a dot. The line indicates the slope derived from Eq. 15; B,D: Spatial fields of two example units in the network with 2% (B) or 10% Gaussian perturbation (D); E: Tracking error, i.e. the difference between the estimated position from the network activity and the actual position of the animal; F: Drift, defined as the absolute value of tracking error, averaged across eight independent simulations. (G–L) Dilution of connectivity by or . The weights are rescaled by after the dilution to keep the strength of the connections comparable to the original connections. G,I: The relation between the velocity of bumps and the velocity of the animal. The same legends are used as in A; H,J: Spatial fields of two example units from the network with 20% (H) or 40% dilution; K: Tracking error; L: Drift.

doi: https://doi.org/10.1371/journal.pcbi.1003558.g005