The first incident, a small grass fire, happened at approximately 20.45 on Sunday, 18 July 2021, in the Inchbroom/Spynie canal area.
The second small grass fire happened around 23:00, also, on Sunday, 18 July 2021, near to Kinneddar House.
Constable Karen Connolly, said:
"Thankfully nobody has been injured as a result of this reckless behaviour. We are keeping an open mind that the two incidents may be connected and are appealing for anyone with information to come forward. We would appeal to anyone who was in the areas at the times who may have seen anything to get in touch."
Constable Connolly has given a description and said:
"We would also ask anyone who saw two males, possibly on bikes, in the area Kinneddar House area around the time to contact us."
Anyone with any information is asked to contact Police Scotland on 101 quoting incident 3537 of Sunday 18 July 2021.
Alternatively those with details can contact CrimeStoppers, anonymously, on 0800555111.