  Klein-Gordon equations describe the dynamics of waves/particles in sub-atomic
scales. For a system of nonlinear Klein-Gordon equations, a systematic analysis
of the time evolution for their spatially uniform solutions has been performed
\cite{21takei}. In the study, the parameters (mass, wave propagation speed, and
the force parameters) are chosen to be symmetric between the two single
equations. Symmetric parameter settings are equivalent to assume the
interacting two same particles. In this paper, for a system of nonlinear
Klein-Gordon equations with asymmetric parameter settings, the time evolution
for their spatially uniform solutions are studied. This is equivalent to assume
the interacting two different particles. As a result, based on the high
precision numerical scheme \cite{22takei}, the existence of divergent and
bounded solutions that depend on parameter settings is revealed. The
competition, coherence, and decoherence of different waves are shown to appear
depending on the choice of asymmetrically-implemented parameter values.
