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The regulation for emission gas of the motorcycle is rapidly being strengthened as the concern about global environment grows around the world, and manufacturers are facing the problem to reduce the toxic materials in the emission gas more. As the technology to reduce the toxic materials, it is common to install a three way catalyst (TWC) on an exhaust system and optimize the oxygen concentration at the inlet of TWC by maintaining air fuel ratio (A/F) on stoichiometric A/F with the control of fuel injection quantity. Furthermore, TWC itself is designed to maintain proper oxygen concentration by the addition of a substance with oxygen storage capacity (OSC), which is able to suppress the variation of the oxygen concentration.