Willie Pietersen, a management professor at Columbia Business School and author of "Strategic Learning: How to Be Smarter Than Your Competition and Turn Key Insights into Competitive Advantage," points to the late Apple founder Steve Jobs.
"Steve Jobs was one of those who was somewhat chaotic as a kind of innovative genius," Pietersen tells CNBC Make It. "[Jobs] was in many cases very cruel to people and very unkind but people gave him a pass on that because of his absolute brilliance, and the excitement and the exhilaration of working behind a brilliant idea."
During Apple's early years, Jobs was fond of calling employees in the middle of the night. If he suddenly had a new idea, he'd completely change everyone's course of action and scrap previous plans.
"[Jobs] was constantly shaking up the organization, constantly striving for new things, rolling over people who didn't agree with him, and sometimes treating them in a brazen and unfair way," says Pietersen. "He was not known as a diplomat in any sense at all."
This chaotic management style proved to be effective for Apple and ultimately led to the creation of highly innovative products, namely the iPad and iPhone. "[Jobs'] mind was very active and very creative," says Pietersen. "And then he hit upon something that was totally brilliant and off it went."
Jobs isn't alone in using chaos to manage others. Pietersen points to start-up founders like SpaceX and Tesla's Elon Musk, Amazon's Jeff Bezos and Facebook's Mark Zuckerberg as successful leaders who had somewhat chaotic management styles at the start of their companies.
However, Pietersen warns that there's a major difference between the leadership style required to run a start-up, whose aim is to be disruptive and innovative, and that of an established organization like IBM. "Would Elon Musk be a candidate to run IBM or General Electric? My answer would be no," says Pietersen.
Start-ups don't have established systems and are much more experimental. They also tend to be led by the same person or group of people who raised the money for the company, which gives them more leeway to be chaotic in the hopes that they become rich and make their investors rich.
"Typically at the beginning of a start-up," says Pietersen, "it's almost necessary to be chaotic because these are ideas that have never been thought out before and there are no underlying structures or systems to make them happen."
But once a start-up transitions into a larger organization, says Pietersen, the leadership team becomes more disciplined and moves away from this chaotic management style. In fact, many start-up founders ultimately sell their company to people who are better suited to run a large organization effectively.
"That's a very good decision at that stage," says Pietersen, "because [they're] not built to run a steady enterprise or a complex enterprise." Meanwhile, companies like Apple whose founders stay on as CEOs are able to remain successful because their business leaders tailor their management style to be more conducive for a large-scale operation.
As for the White House, Pietersen questions whether Trump intentionally uses a chaos-based management style — namely because the U.S. government is not a start-up. "I don't know that it's an explicit philosophy so much as a sense of disorganization," he says.
Intentional or not, Trump's use of chaos has been effective at distracting people from critiquing his policies, says Pfeffer. He likens Trump to a magic act: "One of the things that a magician does is move lots of hands," he tells CNBC Make It. "The intention, of course, is to divert your eyes so you don't see what he or she is really doing. And I think that's pretty much what Trump has been able to accomplish."
The Stanford professor notes that Jobs used a somewhat similar strategy (although in a different context and in a less extreme manner). When a new iPhone release was impending, Jobs would create a frenzied fanfare over the unveiling, leading to speculation about the iPhone's release date, the possible new features and where the launch would take place. This "chaos" kept the public's focus on the newness of the product instead of whether or not the latest iPhone was actually better than the previous one, says Pfeffer.