The nature of pop music is to create phenomena who blaze across the sky like meteors — some of them flaming out, others improbably surpassing their life expectancy.

Make no mistake, many artists trudge on stably for decades, whether superstars such as U2 or performers who fashion solid, lasting careers, such as John Hiatt or Billy Bragg. But new artists who unite fans in their passion and insanity have been a part of pop music for the entire rock era, dating back to Elvis Presley.

Breakout stars in recent years include One Direction and Justin Bieber. Take those last two acts and multiply the hysteria exponentially, and you get what it was like when Duran Duran took over the world in 1982.

Already big in England, Duran Duran helped lead the so-called Second British Invasion of the United States that year, along with acts such as Culture Club, the Human League and Billy Idol. Duran Duran was the biggest of the lot, breaking through with the propulsive disco-rock hit “Hungry Like the Wolf.” A mostly female fan base followed the band all over the place, screamed so loud at concerts that they drowned out the music, and rained stuffed animals, roses and unmentionables upon the band night after night.

On Sunday, nearly 40 years since the band’s beginning, Duran Duran makes its Hawaii debut. The band is touring behind its 14th album, “Paper Gods,” released in 2015.

Duran Duran was big enough to earn the Beatles-evoking nickname “The Fab Five.” In the two years before “Purple Rain,” “Born in the U.S.A.” and “Like a Virgin,” they were as big as anyone this side of Michael Jackson, epitomizing the ’80s look with their teased-out hair, liberal use of makeup and seemingly limitless blazer combos (blazer with collared shirt and tie, blazer with T-shirt, even blazer with nothing underneath).

“It was like being on a wild, wild horse,” bass player John Taylor said last week in a phone conversation from Los Angeles, where he now resides. “You had to hold on very tightly. It happened quickly. It was demanding.”

Those demands have led to some volatility in Duran Duran’s lineup the past 30 years. Taylor was joined by singer Simon Le Bon, keyboardist Nick Rhodes, guitarist Andy Taylor and drummer Roger Taylor in the lineup at the band’s peak. All three of the (unrelated) Taylors have spent time away from the band, but Andy, who left his second stint with the group in 2007, will be the only one missing from Sunday’s show at the Blaisdell Arena.

Hawaii’s Duran Duran fans are a long-suffering bunch. They had their hearts broken in 1994, when the band scheduled a show here but canceled. (Taylor can’t recall the reason, but the band had to cancel or postpone a spate of shows the year before because Le Bon lost his voice.) As a result, Duran Duran has never played a public concert in Hawaii — yet.

“We’ve got a lot to compensate for,” Taylor conceded, adding that the band is excited to finally play here and even planned to arrive a few days early to enjoy themselves a bit and to get Honolulu’s vibe.

After many tours across nearly 40 years, visiting a new place is a rare treat for the band.

“It’s exciting to come somewhere for the first time and really get a beat on the city,” Taylor said. “It’s so special that we’re coming to Hawaii for the first time, because we don’t get to do that too often. … The fact that we’ve never been there is crazy.”

So what can Duranies, as the band’s fans are called, expect in Sunday night’s show? Taylor said the set will cover the band’s entire career.

“It’s weird. When we were getting to the end of our 20s, the end of the ’80s, people were saying, ‘How can you still be playing songs like ‘Girls on Film’? And then you go through this phase where you go, ‘Wait, we’re playing these songs because they’re great songs.’ You’ve really got to own it. You’ve really got to own your legacy.”

Taylor compares a Duran Duran concert to a painter’s retrospective show.

“You’ve gotta tell the artist’s story, the journey. But you want it to be a blockbuster show, so you’ve got to give the people what they want, but you’ve also got to tell the story.”

Lately that has meant leaving out some of their biggest hits. “The Reflex,” the first of the band’s two No. 1 U.S. hits — the title theme from the James Bond film “A View to a Kill” was the other — has not made the cut all year long.

“You do have to rest songs,” Taylor said. “Fortunately, we’ve got enough hits that … I can’t imagine anybody being seriously disappointed if we didn’t play one big hit. I think that just goes with the territory of being a band that’s (been) making records for as long as we have. We just have to make choices.”

Next year marks 40 years for Duran Duran, and Taylor says they have some ideas for commemorating the anniversary, which could include the return of Andy Taylor.

“We’re working on this idea of having 40 events, 40 happenings, to celebrate the genesis of the band,” he said. “When you’ve got a band that’s been around as long as ours, you’ve got two things that you’re focused on. One is legacy; the other is currency.

“You try to make decisions based on the legacy, how do you manage the legacy of the music, and then at the same time, what can you do that feels current, that feels valid. So, you know, we’re looking for ways to do that all the time.”