The first involved a 14-year-old boy who was approached by three men while walking his dog at Stannergate on Saturday, March 13.
On of the men attempted to take the dogs lead.
The first of the men has been described as white, mid 20s, 6ft 1ins and heavy build, wearing all black, and spoke with an Irish accent.
The second was also white, early 20s, 5ft 9ins, slim build, wearing a navy jacket and grey jogging bottoms, and the third was white, early 20s, 5ft 9ins, wearing a North Face puffa jacket and black trousers.
Police are also investigating a second incident where a woman was pushed to the ground by a man who grabbed her dog, but then released it. This happened around 1.15 on Monday, March 15th on the path alongside the Dighty Burn between Drumgeith Park and Baldovie
This person has been described as white, about 30, 5ft 6ins, and medium build, wearing a black hooded top, black snood, black gloves, and had an Irish accent.
Inspector Chris Boath said: “We have officers robustly investigating these incidents, and other incidents which have been reported to us regarding suspicious acts but where no crime has been committed.
"We are also aware of posts on social media groups about incidents which have not been reported to us.
"We understand the concerns of the public regarding these incidents, and would ask anyone who may have been a victim of an attempted theft or have genuine concerns about suspicious acts to please call 101."