  We calculate Shannon information entropy of trapped interacting bosons in
both the position and momentum spaces, $S_r$ and $S_k$ respectively. The total
entropy maintains the fuctional form $S=a + b \ln N$ for repulsive bosons. At
the noninteracting limit the lower bound of entropic uncertainty relation is
also satisfied whereas the diverging behavior of $S_r$ and $S_k$ at the
critical point of collapse for attractive condensate accurately calculates the
stability factor. Next we study the dynamics of Shannon information entropy
with varying interparticle potential. We numerically solve the time-dependent
Gross-Pitaevskii equation and study the influence of increasing nonlinearity in
the dynamics of entropy uncertainty relation (EUR). We observe that for small
nonlinearity the dynamics is regular. With increase in nonlinearity although
Shannon entropy shows large variation in amplitude of the oscillation, the EUR
is maintained throughout time for all cases and it confirms its generality. We
also study the dynamics in a very tight trap when the condensate becomes highly
correlated and strongly inhomogeneous. Time evolution of total entropy exhibits
aperiodic and fluctuating nature in very tight trap. We also calculate
Landsberg's order parameter for various interaction strengths which supports
earlier observation that entropy and order are decoupled.
