Abstract
We expose first a biological model of memory based on one hand of the mechanical oscillations of axons during action potential and on the other hand on the changes in the extra cellular matrix composition when a mechanical strain is applied on it. Due to these changes, the stiffness of the extra cellular matrix along the most excited neurons will increase close to these neurons due to the growth of astrocytes around them and to the elastoplastic behavior of collagen. This will create preferential paths linked to a memory effect. In a second part, we expose a physical model based on random walk of the action potential on the array composed of dendrites and axons. This last model shows that repetition of the same event leads to long time memory of this event and that paradoxical sleep leads to the linking of different events put into memory.