The process of differential memory is quantitatively studied in the modified Harris magnetotail geometry. This process arises as a consequence of nonlinear particle dynamics in the magnetotail which gives rise to partitioning of phase space into disjoint regions. Different regions are occupied by distinct classes of orbits and have widely separated time scales. This paper gives the first study of the time scales and potentially observable signatures in plasma distribution functions associated with the process of differential memory. It is found that the effective ''trapping'' time of stochastic orbits plays a critical role in differential memory and that in the magnetotail geometry, this time has resonances at certain values of the parameter Hˆ. A scaling law Hˆ1/4 has been found for this previously unknown resonance effect. This scaling is directly related to the phase space structures of this stochastic system and leads to signatures in the distribution functions, and their velocity moments (density, velocity components, and kinetic temperatures) are computed following a prescribed change in the boundary conditions. The relationships between the initial changes and the time-asymptotic distribution functions are discussed. The results depend only on the large-scale phase space structures and not on individual chaotic orbits. ¿American Geophysical Union 1991