Republican presidential candidates Ben Carson and Donald Trump at the Republican presidential debate Sept. 16 at the Ronald Reagan Presidential Library in Simi Valley, Calif. (Mark J. Terrill/AP)

The two men could not be more different: One grew up poor and black in Detroit, the other rich and white in Queens. One is soft-spoken and spiritual, the other loud and caustic. Each epitomizes American success, though in vastly different arenas: one as a brain surgeon, the other as a celebrity deal-maker.

But together, Ben Carson and Donald Trump stand as the dominant Republican candidates for president. Their rise and durability — polls show that combined they have the support of 50 percent or more of GOP voters — have befuddled political elites and become the defining dynamic heading into the next debate, Wednesday in Boulder, Colo.

For months, such rivals as Jeb Bush, Marco Rubio and Ted Cruz have assumed that voters eventually will get serious, the outsiders’ stars will flicker out and the real politicians will assume control. Yet, it is late October and that has not happened. By delivering sharp, visceral messages that galvanize the angry electorate, Carson and Trump today are monopolizing the race more than ever.

“The two outsiders have put a blanket over everybody else,” said Doug Gross, a Republican establishment figure in Iowa. “Nobody else can even get oxygen.”

The relationship between Carson, 64, and Trump, 69, has zigzagged from cordial to chummy to cool. They see themselves as kindred spirits, so much so that Trump has said he would consider Carson as his vice president.

At a rally in Jacksonville, Fla. on Saturday, Oct. 24, Republican presidential candidate Donald Trump says both Jeb Bush and Ben Carson have low energy. (Reuters)

Each has resisted bludgeoning the other, but with tensions rising as the kickoff Iowa caucuses draw near, they are starting to take each other on. After fresh polls last week showed Carson leapfrogging Trump for the lead in Iowa, Trump went on the attack.

“We have a breaking story: Donald Trump has fallen to second place behind Ben Carson,” Trump announced Friday night at a rowdy Miami rally. Pausing for dramatic effect, he added, “We informed Ben, but he was sleeping.”

Carson is “super low energy. We need tremendous energy,” Trump thundered, prompting his supporters to break into chants of “USA! USA!” He also said Carson could not create jobs and negotiate trade deals.

Carson shot back, saying at a Saturday event in Iowa: “My energy levels are perfectly fine. . . . There have been many times where I’ve operated 12, 15, 20 hours, and that requires a lot of energy. Doesn’t require a lot of jumping up and down and screaming, but it does require a lot of concentration.”

Trump made the same ­low-energy attack over and over against Bush this summer, and it was a devastating blow to the former Florida governor and onetime establishment front-runner.

Trump kept it up Saturday in Jacksonville, Fla., saying at a riverfront rally: “Carson is lower energy than Bush. I don’t understand what’s going on.” He also singled out Carson’s Seventh-day Adventist faith.

“I’m Presbyterian. Boy, that’s down the middle of the road, folks, in all fairness,” Trump said. “I mean, Seventh-day Adventist I don’t know about. I just don’t know about.”

Carson is prepared for an onslaught from Trump, his advisers said. “It’s a presidential campaign in the United States of America — yes, we expect it,” Carson spokesman Doug Watts said. “We look forward to him making his point of view with the public, and if he does stir it up, we’re all outsiders and anti-Washington, ­anti-establishment, so I think there’s going to be a commonality there.”

Carson plans to take a deliberately gentle approach to his flamboyant foe, said Armstrong Williams, Carson’s confidant and business manager.

“Think about it: Parents, children, employees — they don’t want a boss or a president who is going to fly off the handle and throw insults at people,” Williams said. “People expect you to have a certain level of class and dignity. Wealth does not give you class; it does not give you temperament or discipline.”

The other candidates have seemed hapless, however, in ­taking on Trump. At first, many refused to criticize him. Now, they regularly take potshots at Trump but risk coming across as desperate.

Attacking Carson could also prove difficult, for Trump or any other candidate. In last week’s Washington Post-ABC News poll, 64 percent of Republicans nationally said that the more they heard about Carson, the more they liked him — a higher percentage than for any other candidate in the survey.

In Iowa, a Des Moines ­Register-Bloomberg Politics poll released Friday found Carson with the highest favorability: 84 percent of likely Republican caucus-goers. The same poll had Carson surging past Trump, 28 percent to 19 percent.

“Carson is kind of an unassailable candidate,” said Steve Deace, a conservative radio host who is supporting Cruz, the Texas senator. “Even if people don’t think Carson is ready to lead, they still see him as a symbol of what we once were and should be again — the kind of country that produces Ben Carsons.”

In the media, Carson has come under fire for controversial comments, including his remarks that Muslims should not be allowed to serve as president, and that Adolf Hitler might have been stopped had the German public been armed. But the Iowa poll showed voters agreeing on these points. “What we’ve found is that he’s not popular in spite of these vivid things he’s said; he’s popular because of them,” said J. Ann Selzer, who conducted the survey.

Because of Carson’s popularity, top Republicans say, taking him down will require precision and care. “I don’t think that you need to attack him; you just need to examine him,” Gross said. “While he has an awesome bedside manner for a sick patient, you really wouldn’t ask a politician to do brain surgery. Would you ask a brain surgeon to fix the country?”

After raising more money in the most recent quarter than any other Republican candidate, Carson began a television advertising blitz in the four early states last week. Watts said the campaign will stay on the air through the spring and is reserving time in states with March contests. So far, his spots are positive introductory messages that end with his slogan: “Heal. Inspire. Revive.”

Earlier this month, Trump told The Washington Post that he would spend upward of $20 million on TV ads and was developing concepts with a Florida-based media firm. Reacting to Carson’s rise, Trump’s allies are urging him to air his own ads immediately.

“Now is the moment we knew was going to come,” said Roger Stone, a former Trump adviser. “He needs to get on the air. The whole point of political messaging is repetition, and if Carson continues to rise in places, and negative ads begin to air against [Trump], doing a one-time shot on ‘Morning Joe’ to counter it won’t be enough.”

The emerging skirmish is not the first between Carson and Trump. Carson, who built a powerful following with evangelicals, stunned Trump in early September when he questioned Trump’s faith. He said Trump did not appear to have the “humility and the fear of the Lord.”

Trump counter-punched, mocking the famed neurosurgeon as a mediocre, everyday doctor who has only “hired one nurse.”

Almost immediately, they patched things up. “We didn’t want that fight,” said Corey ­Lewandowski, Trump’s campaign manager. “It was an isolated incident, really. We’ve moved on.”

Since then, Trump and Carson labored to avoid another clash. Their campaigns were allies in negotiating the conditions with CNBC for this week’s debate. Phone calls and e-mails between the camps are friendly, signaling not so much an alliance as a bond between the cycle’s most unorthodox candidates.

“We’ve hit a chord, and we’re not as different as people think,” Trump told CNN this past week. He speculated about sharing the Republican ticket with Carson: “Stranger things have happened.”

Trump and Carson’s relationship predated the campaign. They are neighbors in West Palm Beach, Fla., where associates introduced them. Their first extended exchange was at a dinner in April 2013, shortly after Carson and his wife, Candy, moved from their longtime home in Maryland. The Carsons envisioned a peaceful retirement in the columned mansion they bought on the 17th hole at the elite Ibis Golf and Country Club.

Trump’s luxury Mar-a-Lago golf resort was a 15-minute drive away and, at the urging of Newsmax editor Christopher Ruddy, a mutual friend, Trump invited the Carsons over for dinner.

Two months prior, Carson lighted up the political right by criticizing President Obama at the National Prayer Breakfast. At Mar-a-Lago, the Carsons, Trump and Ruddy mingled with Dror Paley, a Canadian orthopedic surgeon, and children who have health issues. During the dinner, Trump and Carson talked about Carson’s move, his career in medicine and Trump’s various activities. They discussed Carson’s speech about Obama. The country was in trouble, they agreed, and Obama’s presidency was a disaster. But their connection ended there, according to Williams.

“They didn’t get into family values and struggles,” he said. “These kinds of conversations can sometimes feel like a production, like meeting an image and a brand.”

Asked to assess the candidates’ rapport, Lewandowski was circumspect.

“They respect each other,” he said, “but there can only be one winner.”

Rucker reported from Des Moines, and Costa reported from Washington. Sean Sullivan in Miami and Jacksonville, and Jenna Johnson in Washington contributed to this report.