The incidents happened on the Pennypack Trail in Northeast Philadelphia.
"It seems that this male may suffer from some type of mental illness," said Insp. DeShawn Beaufort. "Without provocation from the victims, just immediately attacked them while they were on the trail."
The first attack happened around 8:15 a.m. on Nov. 22 in the area of 2800 Holme Ave.
Police say the victim was running on the trail and was approaching a bicyclist from behind.
As the runner announced his approach the bicyclist became enraged.
The victim said that the bicyclist pulled out a large knife, possibly a machete, and slashed him multiple times in the arms and hands. He was treated for his injuries at Nazareth Hospital.
Then, around 9 a.m. on Nov. 24, two people were walking along the trail in the area of 2800 Winchester Avenue when one of them was attacked by a bicyclist with a large knife.
The male victim was cut on his right arm and hands. He was treated for his injuries at Jefferson-Torresdale Hospital.
Police say a female recently contacted detectives to say she encountered a man on a black bicycle who became agitated and started yelling at her on the morning of Nov. 25.
The man tried to retrieve something that was tied to the bike, but she ran away and was not injured.
"It's nerve-wracking. We got kids that come down to the park, families, and for this to happen - something has got to be done about it," said Noah Jacobs of Northeast Philadelphia.
Authorities say there have been no incidents reported since Nov. 25, and police note that patrols have been stepped-up in the area.
The suspect was described as a Hispanic man between 40 and 60 years old. He has a thin build, weighed about 180 pounds, and was said to be wearing dark clothes in some of the incidents.
His bicycle was described by some of the victims as a "BMX-style" bike.
Anyone with information can contact Philadelphia police at 215-686-TIPS (8477).