  Integrable deformations of a class of Rikitake dynamical systems are
constructed by deforming their underlying Lie-Poisson Hamiltonian structures,
which are considered linearizations of Poisson--Lie structures on certain
(dual) Lie groups. By taking into account that there exists a one-to one
correspondence between Poisson--Lie groups and Lie bialgebra structures, a
number of deformed Poisson coalgebras can be obtained, which allow the
construction of integrable deformations of coupled Rikitake systems. Moreover,
the integrals of the motion for these coupled systems can be explicitly
obtained by means of the deformed coproduct map. The same procedure can be also
applied when the initial system is bi-Hamiltonian with respect to two different
Lie-Poisson algebras. In this case, to preserve a bi-Hamiltonian structure
under deformation, a common Lie bialgebra structure for the two Lie-Poisson
structures has to be found. Coupled dynamical systems arising from this
bi-Hamiltonian deformation scheme are also presented, and the use of collective
`cluster variables', turns out to be enlightening in order to analyse their
dynamical behaviour. As a general feature, the approach here presented provides
a novel connection between Lie bialgebras and integrable dynamical systems.
