  The pi N --> KY and KY --> KY reactions are studied using a dynamical
coupled-channel model of meson-baryon interactions at energies where the baryon
resonances are strongly excited. The channels included are: pi N, K \Lambda,
and K\Sigma. The resonances considered are: N^* [S_{11}(1650), P_{11}(1710),
P_{13}(1720),D_{13}(1700)]; \Delta^* [S_{31}(1900), P_{31}(1910),
P_{33}(1920)]; \Lambda ^* [S_{01}(1670), P_{01}(1810)] \Sigma^* [P_{11}(1660),
D_{13}(1670)]; and K^*(892). The basic non-resonant \pi N --> KY and KY --> KY
transition potentials are derived from effective Lagrangians using a unitary
transformation method. The dynamical coupled-channel equations are simplified
by parametrizing the pi N -->pi N amplitudes in terms of empirical pi N
partial-wave amplitudes and a phenomenological off-shell function. Two models
have been constructed. Model A is built by fixing all coupling constants and
resonance parameters using SU(3) symmetry, the Particle Data Group values, and
results from a constituent quark model. Model B is obtained by allowing most of
the parameters to vary around the values of model A in fitting the data. Good
fits to the available data for pi^- p to K^0 \Lambda, K^0 \Sigma^0 have been
achieved. The investigated kinematics region in the center-of-mass frame goes
from threshold to 2.5 GeV. The constructed models can be imbedded into
associated dynamical coupled-channel studies of kaon photo- and
electro-production reactions.
