[Toto]

You may have inherited an IP address that was assigned to a computer and was running some sort of service, and maybe the connecting IP's are trying to call home as it where.

Have you annoyed anyone in a public forum and they could see your IP address?

Maybe you were acting as a server for some peer to peer system?

Loads of possible causes really. May be worth checking your router logs to see if there is a pattern to the port the various IP's are trying to connect to.

Of course it may not be a DoS attack, but without bit of digging around in there, there is no way of telling.