The victims - which also included two women and two men in their 30s - were all expected to survive, though one of the women was listed in critical condition.
Witnesses heard screaming and a child crying at about 8 a.m. in Riverside Park along the Hudson River near West 65th Street, an elegantly landscaped stretch of greenery flanked by luxury residential high-rises.
After the surprise attack on a sunny fall morning, officers grabbed the suspect and took him into custody.
Police Commissioner Raymond Kelly identified him as Julius Graham, a 43-year-old Texas native who had been living in a Bronx shelter. He used half a pair of scissors in the attack, Kelly said. KTRK's sister station, WABC-TV in New York, says Graham lived in Houston.
According to the police commissioner, Graham first approached a 36-year-old jogger and stabbed her in the back. He also attacked a 36-year-old man walking his dog, then a 32-year-old woman running along the path, stabbing her in the neck.
Finally, Graham attacked a 35-year-old man pushing his son in a stroller, Kelly said. He stabbed the man in the chest as he faced the attacker to protect his son and slashed in the boy in the arm, Kelly said.
Graham was taken to Bellevue Hospital for evaluation.
Geoffrey Croft, a spokesman for New York City Park Advocates, called the attack the latest episode in a "troubling trend" of violence in city parks.
He noted that a mother pushing a stroller along the Henry Hudson Parkway in Fort Tryon Park in Upper Manhattan was attacked by a homeless man last week. At least two bicyclists were attacked a week apart in August along the Hudson River around 163rd Street, and two other people were slashed south of 60th Street a month earlier, Croft said.
Croft said the advocacy group has been calling for more park enforcement for years. Citywide, he said there are 80 security officers patrolling the city's parks, with another 80 recently hired. In the 1990s, there were 450 parks security officers, he said.
When asked about the spate of recent attacks, the police commissioner said city parks are "very, very safe." He said that although authorities are concerned about the recent crime, "the amount of incidents of crime in parks is minuscule."
Jason Santos, a 21-year-old biker from Queens, said he wouldn't use the bike path as much because of the most recent attack.
Edlin Pitts, a Manhattan resident who uses the path daily, said he had been cognizant of safety at night, "but this happened during the day, and I'm concerned."
"I'll just try to be more aware now - and I won't let this stop me," he added.
Yellow police tape and park security on Tuesday closed access to the path. All that was left from the attack was the child's stroller, abandoned in the park.
The Associated Press contributed to this report
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