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the AFR "cycles" for two very important reasons....
#1 being that it's how the narrowband sensors are used to correct for fueling. if the sensor is constantly sitting near any one value, it's indicating that the sensing element is dead, it's not up to operating temperature or an extremely rich or lean condition is present. by forcing the AFR to "swing" around stoich, the ECM will cause the AFR to average stoich by attempting to make the time above and below the reference voltage equal.
#2 is the cat itself... supposedly they operate more efficiently when they are put into situations of slighty rich followed by slightly lean.... i really don't understand why, but it's been suggested that it needs some extra oxygen inside it to help the reactions. if this were the case, an AIR system that pumps air into the cat nearly all of the time would probably work quite well. or at least get it hot and keep it that way very quickly, though it wouldn't hurt to estimate cat temp so not to overheat it.
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