No one has claimed responsibility for the 6in-long incendiary devices.
But they are said to be almost identical to those planted by the IRA in attacks in Blackpool, Brent Cross and Gateshead earlier this year.
They were set to explode at varying intervals throughout Thursday night but only two went off, causing limited damage to the town's Habitat shop and BhS. The others were found by bomb squad officers.
One device was planted under a shelf in the city's Beatties toy shop and three others were hidden behind books in the nearby reference library.
Two more were found in the John Lewis store.
Detective Sergeant Tony Everitt said: 'This sort of appeal is unheard of.
'We want to hear from everyone who went into those shops on Thursday between 9am and 5pm.'
Shoppers are asked to ring local police on 0908 686268.Reuse content