Sonic - Capoeira
The way he spins and does breakdance moves every time. This is the closest fighting style resembling Sonic's fighting style (excluding the homing attacks of course)
Knuckles - American Boxing
I WAS gonna say Muey Tai, but Knuckles barely does kicks. Also his punches are more powerful then they are fast.
Shadow - Karate
This is judging from Sonic Battle because other games he tends to kinda fight like Sonic. I see him using chops and roundhouse kicks. Also his Chaos Attacks still kinda resemble attacks like an Elbow Slam.
Tails - Ballet? Breakdancing?!
I have no idea, his most famous attacks are spinning around, but you see him spin on his hands a little while spinning in Sonic Adventure DX. Looks like he mixes Ballet with Breakdancing to attack. Now I know they're not actual fighting styles, but attacking with a Tu Tu is allot more resembling Tails' use of his tails then someone spinning around doing Roundhouse kicks.
There are more characters but these are examples. Of course, some people know more fighting styles so maybe they know better resembling fighting styles to categorize it to the characters.
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