In this paper we are interested in the convergence of accumulation of dislocations to walls of dislocations. We consider the dynamical system generated by the force $f(x,y)=\frac{x(y^{2}-x^{2})}{(y^{2}+x^{2})^{2}}$, defined over $\R\times\Z\backslash{0},$ that describes the phenomena. For initial data $X^{0}\in\Omega\cap\ell^{\infty}=\left{X: |x_{i} - x_{j}| \leqslant \sqrt{3 - 2\sqrt{2}} \,|i-j| \right}\cap\ell^{\infty},$ we show %% using Cauchy Lipschitz theorem the existence of unique solution $X\in C^{1}\in([0,+\infty),\Omega\cap\ell^{\infty}).$ Moreover, we prove that if $X^{0}$ is periodic, then $X(t)=(x_{j}(t)){j\in\Z}$ is periodic for any $t>0$ and converges to the barycenter of the initial data, i.e. $x{j}(t)\to c=\frac{1}{N}\sum_{i=1}^{N}x_{i}^{0}$ for every $j\in\Z.$ We also establish a $\ell^{p}$ contraction for periodic solutions and perform numerical simulations.
