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A small university city in northern California is on edge after three people were stabbed within a week.

Two of the stabbings were fatal, killing a college student at the University of California, Davis and a homeless person.

In the most recent incident on Monday, a homeless woman was knifed several times through her tent.

No arrests have been made, and police in Davis have not said if they are searching for one or multiple suspects.

"People are scared," Mayor Will Arnold said at a press conference on Tuesday.

Davis Police Chief Darren Pytel said "the attacks were particularly violent and brazen", adding that in the two most recent stabbings the "suspect didn't seem to care there were several witnesses".

He said he could not recall any incidents like this in his four decades working on the city's police force.

Mr Pytel said the first victim, 50-year-old David Henry Breaux, was found on Thursday on a bench where he often ate and slept.

The second victim was 20-year-old student Karim Abou Najm. The computer science major was six weeks away from graduating before he was stabbed to death at Sycamore Park on Saturday evening.

The third stabbing occurred shortly before midnight on Monday at a homeless encampment. The victim, who has not been named, was stabbed several times through her tent and is in a critical condition, Mr Pytel said.

Police issued a shelter-in-place order after the most recent stabbing but lifted it hours later with no sign of a suspect.

The attacker has been described as a male with long curly hair and a thin build, Mr Pytel said, a description which he said was similar to that of the suspect in the second stabbing.

He urged residents to be careful and to remain vigilant, adding that his department was working through hundreds of tips and looking for DNA evidence.

"This is too much," one student wrote on Twitter. "I'm looking around at my peers terrified at the possibilities. This is traumatic."

The FBI and other law enforcement agencies are assisting the Davis Police Department.

"I am freaked out about it," Nikki Moreno, a UC Davis student, told The Sacramento Bee newspaper. "I think after this third one, I am more fearful. It doesn't seem like this is a person who's targeting people."

Gary May, chancellor at UC Davis, released a statement on Tuesday briefing students on updated security measures. They include moving all classes ending after 18:00 online and installing additional security cameras.

"I assure you the safety of our campus community is our top priority as we deal with the rash of violent stabbings in Davis," Mr May said.