Integration of Additive Self-Motion Inputs in a General Bump Attractor Model.

Path integration is a navigational strategy through which an animal remains oriented even in the absence of stable landmarks. Bump attractor networks have played a key role in modeling and analyzing the neural processes involved in path integration. In such networks, self-motion inputs and asymmetries in the network translate an activity bump over the attractor manifold, updating the animal's perceived position in space. The self-motion inputs can be incorporated through a multiplicative model, in which neuronal inputs are combined multiplicatively, or an additive model, in which neuronal inputs are combined through summation. Multiplicative models have a simple traveling wave solution and are often used to analyze properties of these networks. Relatively little mathematical analysis has been done on additive models, which are generally considered to be more biologically realistic. We analyze a general additive bump attractor model of path integration, deriving explicit mathematical expressions describing the temporal and spatial dynamics of the activity bump. We find that intrinsic spatial deformations of the activity bump lead to small, positive path integration errors that are approximately proportional to the animal's velocity. This error is minimized through a balance of acceleration and velocity input. We also derive simple expressions for the path integration gain, showing explicitly how it depends on the model parameters. Our analytical results are supported by numerical simulations of four specific, representative models. Our results have biological implications and provide a mathematical foundation for understanding a large class of path integration models. [ABSTRACT FROM AUTHOR]