be viewed as *an attractor*, since similar effects are observed in neural network models studied in [@KMR] and [@MalTur]. In fact, the Markov chain $v(t)$ describes the same dynamics as the neural network models in [@KMR] and [@MalTur] though in a slightly different set-up. The difference seems to be technical but it results in quite different model behaviour. We do not investigate this issue in depth here.

Table \[Tabl2\] contains the list of all possible limiting configurations (for proportions of customers/particles) for small $M$, while in Table \[Tabl3\] we provide only the numbers of possible limiting configurations for some larger $M$. Note that in the tables the symbol ${}^*$ stands for the configurations which cannot be achieved from the empty initial configuration. Unfortunately, we cannot compute exact numbers of possible limiting configurations for any $M$; nor can we predict which of them will be more likely (though it is obvious that if we start with the empty initial configuration, all possible limits which can be obtained by a rotation of the same ${\bf x}$ will have the same probability.)

Asymmetric interaction
----------------------

In the asymmetric case the potential of site $k$ at time $t$ is $$u_k(t)=\xi_k(t)+\xi_{k+1}(t),\, k\in\M.$$ The transition probabilities 