  A system of traps is considered, each containing a large number of
Bose-condensed atoms. This ensemble of traps is subject to the action of an
external modulating field generating nonequilibrium nonground-state
condensates. When the frequency of the modulating field is in resonance with
the transition frequency between two different topological coherent modes, each
trap becomes an analog of a finite-level resonant atom. Similarly to the case
of atoms in an electromagnetic resonant field, one can create entanglement
between atomic traps subject to a common resonant modulating field generating
higher coherent modes in each of the traps. A method is suggested for
regulating entanglement production in such a system of multitrap and multimode
Bose-Einstein condensates coupled through a common resonant modulating field.
Several regimes of evolutional entanglement production, regulated by
manipulating the external field, are illustrated by numerical calculations.
