  We study the nonlocal non-Markovian effects through local interactions
between two subsystems and the corresponding two environments. It has been
found that the initial correlations between two environments can turn a
Markovian to a non-Markovian regime with the extra control on the local
interaction time. We further research the nonlocal non-Markovian effects from
two situations: without extra control, the nonlocal non-Markovian effects only
appear under the condition that two local dynamics are
non-Markovian-non-Markovian(both of two local dynamics are non-Markovian), or
Markovian-non-Markovian, never appear under the condition of
Markovian-Markovian; with extra control, the nonlocal non-Markovian effects can
occur under the condition of Markovian-Markovian. It shows that the
correlations between two environments has an upper bound: only making a flow of
information from the environment back to the global system begin finitely
earlier than that back to any one of two local systems, not infinitely. Then,
due to observing that the classical correlations between two environments have
the same function as the quantum correlations, we advise two special ways to
distribute classical correlations between two environments without initial
correlations. Finally, from numerical solutions in the spin star configuration
we obtain that the self-correlation(internal correlation) of each environment
promotes the nonlocal non-Markovian effects.
