Denmark has long been a model country: Some of its political initiatives have sounded more like fiction than reality, and too good to be true. The country's higher education system, for instance, entitles every Danish student to a monthly payment of about $900.

But there is another side to Denmark: It is also a country Syrian refugees want to leave behind as quickly as possible, even if it means walking to the border.

On Monday, authorities placed an ad in Lebanese newspapers carrying  an unspoken yet unmistakable message to migrants: Don't come to Denmark.

In fact, few really want to stay in the country, but they need to pass through Denmark to reach Sweden, which has so far accepted the most refugees per capita among all European countries. Most of the migrants in Denmark are hoping to reunite with family members or friends in Sweden. "Sweden already has accepted far more refugees than Denmark. So those arriving later are more likely to find these social networks there," said Zachary Whyte, an asylum and integration researcher at the University of Copenhagen.

The Danish government recently cut welfare benefits for refugees and now only allows family reunifications after a one-year delay. "For refugees that have left behind their families in war zones or other precarious circumstances, a year is a long time," Whyte said. But he added that the Danish reception system isn't nearly as tough as its reputation.

On Wednesday, however, Danish authorities stopped all trains connecting the country to continental Europe through Germany in order to prevent refugees from crossing the border. Meanwhile, refugees who were already in the country refused to register because they feared having to stay. Most were transferred to a school in Padborg, but 300 of them decided to leave.

Danish police officers did not attempt to stop the people who left the school refugee center, and they did not use violence. The school "is not a prison and there is no fence around it," local police was quoted as saying in a statement by Danish news site The Local.

Denmark's neighbors are worried

The Danish government's current strategy will probably make it harder for Denmark to collaborate with other E.U. countries. Germany and Sweden have had harsh words for their neighbor: "Denmark is a rich country and is able to take care of the refugees," the Swedish justice minister said, responding to demands from the Danish government that Sweden accept some of the refugees in Denmark.

"The strong anti-refugee stance of Denmark is not a surprise, given the new government that is in place since June," said Astrid Ziebarth, a migration fellow at the German Marshall Fund, a political think tank. Ziebarth was referring to the center-right minority government that has governed the Scandinavian country for the last three months, backed by the populist anti-immigrant Danish Peoples Party, which won 21 percent of the votes.

"At least since the early 2000s, the prevailing analysis among the political parties has been that elections can be won or lost on the issue of immigration," said Whyte, the migration researcher. Denmark is already among the few E.U. countries that have opted out of the common asylum system which is supposed to allocate refugees fairly among member states.

Some Danes press for change

Given the reluctance of Denmark's political parties to welcome more refugees, some Danes have taken matters into their own hands. "The restrictive policies on asylum and refugee issues have sparked a mobilization among the country's civil society. People donate or buy warm clothes, whereas a smaller group of Danes are actually trying to pick up refugees in their cars to drive them either across the bridge to Sweden or at least to a train station that will enable them to cross," Whyte said. He predicted that such activism could force the government to reconsider its stance, and has already led to minor disagreements between the ruling Liberal Party and its largest backer, the Danish People’s Party.

But for now, all major political parties in Copenhagen are pulling "in the same direction of tightening the laws," Ziebarth said.

Until recently, Copenhagen branded itself as tolerant and friendly to foreigners, using the slogan cOPENhagen. These days, many foreigners might not see it that way.