Early experiments studying the effects of lesions of the Hippocampus have reported that recent memories are often unavailable to be retrieved, while old memories are successfully reminded. These observations have led to state the theory of Systems Consolidation. This is the process by which the fast-learning Hippocampus replays the encoded memory during sleep and thus consolidates the corresponding memory in the Neocortex [1]. Formation of memory would take longer in the Neocortex because of its much larger spatial scale compared to the Hippocampus, and thus requires axonal growth and synaptogenesis. Finally neurogenesis in the Dentate Gyrus could explain the forgetting in the Hippocampus [2]. In fact newborn neurons alter hippocampal circuits, thus decreasing the probability to retrieve memory and eventually leading to its clearance. We propose here a neural fields model to assess whether the above hypotheses are enough to explain the basis of Systems Memory Consolidation. We considered three 1D connected neural fields, the Neocortex (long-term memory), the areas CA3-CA1 of the Hippocampus (short-term memory) and the Dentate Gyrus, also part of the Hippocampus. We were interested in the formation of connections between two distinct bumps of activity, which represent two distant parts of the memory pattern. Our study suggests that the crucial element for the rate of consolidation would be the initial density of connections between the parts of the pattern. Furthermore the rate of neurogenesis seems to determine the persistance time of a memory in CA3-CA1 before its clearance. We plan in the future to use this study to grasp the origins of dysfunctions of memory consolidation processes.