Before revision: The purpose of this paper is to understand how the grid cells may perform path integration calculations . We study a general representational model of path integration in which the self-position is represented by a vector formed by the activities of a population of grid cells , and the  self-motion is represented by the change of this vector which is transformed by a general recurrent network for path integration.
After revision: The purpose of this paper is to understand how the grid cells may perform path integration calculations remains a fundamental problem. In this paper, we conduct theoretical analysis of a general representation model of path integration in which the self-position is represented by a vector formed by the activities of a population of grid cells , and the self-motion is represented by the change of this vector which is transformed by a general recurrent network for path integration.