Abstract
In this paper we constructd the positive permutation braid of pump-modulated Nd-doped fiber laser dynamics and denoted it by $\beta _{n,k,r}^{+}$ . We study this braid as a permutation, then calculate its inversion matrix. The braid representatives $\beta _{n,k,r}^{+}$ of the orbits associated to a modulated Nd-doped fiber laser as a permutation are given. It is shown that pump-modulated Nd-doped fiber laser knots and links are positive permutation braid.
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