annual, daily, monthly, seasonal, weekly
the annual cycle of church festivals

irregular, regular
women with irregular menstrual cycles

complete, entire, whole
continuous, endless, never-ending
the endless cycle of birth, death and rebirth

natural
Life is a natural cycle, just like the changing seasons.

vicious
caught up in a vicious cycle of bingeing and dieting

virtuous
lunar, solar
the 76-year solar cycle

carbon, water
a diagram of the water cycle

breeding, menstrual, reproductive
sleep
business, economic
boom-and-bust
development
election (AmE)
news (esp. AmE)
life
the life cycle of the butterfly

follow, go through
The market is simply going through an economic cycle.

complete
To complete the cycle, oxygen is necessary.

repeat
break, end, stop
create, start
continue, perpetuate

begin again
Male and female adults mate, the female lays eggs, and the cycle begins all over again.

continue, repeat (itself)
This cycle of events continually repeats itself.

length, time

in a/the cycle
at this point in the cycle

per cycle
The number of young produced per breeding cycle varies from species to species.

a cycle of abuse, poverty, violence, etc.
part of the cycle (of sth)
part of the cycle of birth and death

motor (usually motorcycle), pedal

ride

ride
We're going for a cycle ride this afternoon.

helmet
lane, path, route, track
Cars are not allowed in the cycle lanes.

race