Paralyse and paralyze are different spellings of the same verb. Paralyze is preferred in the U.S. and Canada. Paralyse is preferred outside North America. The distinction extends to derivative words such as paralysed/paralyzed and paralysing/paralyzing.
The noun paralysis is spelled the same in all varieties of English. And, incidentally, paralysation and paralyzation are unnecessary words for paralysis.
Examples
For example, these North American publications prefer paralyze:
With the bond severed between fearful memory and its object, a phobia loses its power to paralyze. [Los Angeles Times]
Opposition members are threatening to withdraw their support of the Speaker, which would paralyze the National Assembly. [Globe and Mail]
Patients remain in an unconscious, paralyzed state for at least 24 hours and then the body is allowed to slowly warm. [Arizona Republic]
And these British and Australian publications use paralyse:
But while Iraq should inform us, it should not paralyse us. [Guardian]
Gillard is doing enough on her lonesome to paralyse her government. [Sydney Morning Herald]
This town is not the only area of Tamaulipas, a state of the size of the Czech Republic, virtually paralysed by violence. [BBC]
