We study some effects of spatial inhomogeneity and external forcing on spiral waves in the FitzHugh-Nagumo equation and attempt in a numerical investigation to eliminate spiral patterns using "entrainment" and "trapping". We find that a target pattern generated by circular fast pacemaker region can overwhelm a spiral pattern and eliminate spiral waves. We also find that a spiral pattern can be trapped in a less excitable region. Through control of this less excitable region, a pair of spirals can be annihilated. In addition, it is shown that spiral waves are entrained and disappear under a spatially uniform periodic forcing if the forcing is sufficiently strong. We discuss two mechanisms causing complete entrainment.
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