Let us assume a dynamic system which has vector with 'n' components (which are non-negative integers from 1->n) at time t=1. In other words we have a permutation over 1->n at time t=1. Assuming time to be discrete, at any time time 't' , the system evolves such that there are 't' permutations with 'n' components in each. We do not know in advance which permutations in time 't' contributes to the birth of which permutation in time 't+1'. We can assume that each permutation in time 't+1' has a probabilty distribution over the permutation in time 't' for being its parent. The only information available is the permutations at each time instance from 1 to T. What kind of models can be used to represent such a system if we want to find out if the permutations attain a stable state with very less perturbations after certain time period?