This pattern, which I call the “Thucydides Trap,” recurs often. A major nation’s rise has disrupted the position of a dominant state 16 times over the past 500 years. In 12 of those 16 cases, the outcome was war. In the four cases that avoided violent conflict, that was possible only because of huge, painful adjustments in attitudes and actions on the part of challenger and challenged. Think of Britain and the United States under Theodore Roosevelt, or the United States and the Soviet Union during the Cold War.

We are certain to see a succession of confrontations between China and the United States in the years ahead. What is in doubt is whether the leaders of these two great powers can manage these confrontations without escalating them to war. For now, that’s up to Trump and Xi.

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If Hollywood made a movie pitting the United States against China on the road to war, central casting would be hard-pressed to find two better leads. As personalities, Trump and Xi could not be more different. Despite the formalities of a scripted summit, their contrasting styles will be on full display. But in many ways, they are mirror images of each other.

Both have pledged to restore the greatness of their nations with an agenda of radical change. Everyone knows Trump’s trademark one-liner. But when Xi rose to power in 2012, he announced his “China Dream,” calling for “the great rejuvenation of the Chinese nation.”

Both men take pride in what they consider their unique leadership capabilities. Trump built his presidential aspirations on what he portrayed as unrivaled business acumen, memorably claiming that he alone could fix the nation’s problems. Xi has so firmly concentrated power in his own hands that he is now often referred to as the “Chairman of Everything.” Indeed, the exceptionalism ingrained in each man’s political agenda speaks to a broader similarity between the United States and China: Both have extreme superiority complexes. Each sees itself as without peers.

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And, perhaps most important, both Trump and Xi view the nation the other leads as the principal obstacle to achieving their core ambition.

The danger is that amid the structural stress caused by China’s rise, and exaggerated by Xi’s and Trump’s clashing visions, inevitable crises that could otherwise be contained will result in outcomes neither side wants.

The potential sparks for such a conflict are frighteningly mundane. Already during the Trump administration, tensions have escalated over the status of Taiwan, North Korea’s nuclear ambitions and trade. (During his campaign, Trump accused China of “raping” the U.S. economy. On Thursday, he tweeted that the meeting with Xi “will be a very difficult one,” because “we can no longer have massive trade deficits and job losses.”)

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Could a trade conflict become a hot war that ends with nuclear explosions? As preposterous as that may sound, remember that Japan’s attack on Pearl Harbor happened after the United States imposed crippling sanctions on Japan, bringing this country into a war that ended with atomic bombs on Hiroshima and Nagasaki.

The straightest path to war between the United States and China would begin with a sharp turn by Taiwan toward independence. During the presidential transition, Trump tripped this alarm with tweets and a phone call with Taiwan’s leader. No Chinese national security official I have ever met, and no U.S. official who has examined the situation, doubts that China would choose war over losing territory it considers vital to its national interest. Were a Taiwanese president, with or without encouragement from Trump, to cross one of Beijing’s bright red lines, China might begin with an updated version of its 1996 “missile tests” that bracketed Taiwan. If the United States came to Taiwan’s assistance and provided Navy escorts for the lifeline of ships supplying the island, China could try to sink one or more. And to prevent China from suppressing Taiwan, the United States would have to conduct massive, repeated attacks on missile bases on the Chinese mainland, killing thousands of Chinese. It’s hard to believe that China would not respond to such attacks with equivalent strikes on U.S. air bases in Guam and Japan, as well as carriers. From there to bombs exploding on U.S. soil is not a very long hop, skip or jump.

North Korea is another possible catalyst for a war no one wants — but nonetheless could happen. During the upcoming summit, Trump is expected to demand that Xi put more pressure on Kim Jong-un to rein in his nuclear program. On its current path, North Korea will acquire the capability to deliver a nuclear weapon against the U.S. homeland on Trump’s watch. The president has said he won’t allow this to happen. The Pentagon has reportedly prepared various military options to slow North Korea’s missile program. Although some might hope that fallout from a surgical strike would be limited, a U.S. attack could provoke retaliation that triggers a second Korean War or the collapse of the Kim regime. Either could lead to war between the United States and China.

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U.S. war planners have examined scenarios for North Korea that begin with regime collapse. As the country descends into chaos, U.S. forces would try to destroy weapon systems capable of delivering a nuclear warhead against South Korea, Japan or Guam. The U.S. Joint Special Operations Command has a long-standing mission to secure “loose nukes” and has trained to enter the North to take control of its nuclear weapons facilities before rogue commanders could pirate these weapons to international arms bazaars. But because the sites are thought to be near China’s borders, it is likely that Chinese special forces would beat U.S. forces there. As Gen. Raymond Thomas, a former head of the Joint Special Operations Command, has warned, trying to secure North Korea’s nuclear weapons would result in a “vertical track meet” between Chinese and U.S.-South Korean forces. Unaware of each other’s presence, they could end up in a firefight and mistake accidental engagement for an intentional ambush requiring retaliation.

Another possibility is that, after a regime collapse, North Korean refugees would pour into China. Fearing its own instability, China could send troops into North Korea and establish a buffer state between it and South Korea. Under pressure from its population to liberate those who have lived under the most brutal regime on Earth, the South Korean government could also send troops marching north. Because U.S. troops and aircraft stationed in South Korea are integrated with South Korean troops in operational military plans, American and Chinese troops would then engage one another directly, as they did in 1950.

Is it possible to manage the structural stress between rising and ruling powers without war? Yes. Xi and President Barack Obama even discussed the Thucydides Trap at their 2015 summit, but could not agree what to do to escape it. Xi had proposed a “new form of great power relations.” But by this he meant an expansive concept of China’s core interests, including an Asian sphere of influence, which the United States could not accept.