Fur doesn't have same position after closing and opening blender again

Hello
I’m working on a animation of an animal with fur. If i render my full animation everything is fine, but if i close and open blender again there is a slight difference in position of the fur, this is really small, but enough to be visible. If i update my animation i would like to be able to render only the updated part and not the whole animation. I’m using blender 3.1, i’m not using any physics or collision (exept what i’m forced to use to work with hair), I have been looking around and couldn’t find anyone who had the same problem or any info about it. I guess there is a random value somewhere witch is not connected to the random seed.
So here i am asking here if anyone got a solution for that, as my animation is getting bigger, solving that issue will save me a lot of rendering time.

here is my particle setup :

other part of the particle setup: