In the past, Mr. Modi has bragged about having a 56-inch chest measurement, apparently a symbol of strength. But that swagger was bruised last year after Chinese troops swept into a disputed area along the Bhutan-China border near to where Indian troops were based and started building a road. When India objected, China threatened to “teach India a lesson.”
China’s military power dwarfs India’s, and very quickly, Mr. Modi, who is seen here in India as something of a strongman, was faced with a challenge he could not easily contain.
A flurry of diplomatic efforts between the two countries cooled things down. But analysts say Mr. Modi urgently wants to avoid another confrontation with his powerful neighbor, especially now. Though his political party is still India’s most formidable, a few missteps in recent weeks, including a delayed response to two highly publicized rapes, have brought an avalanche of criticism.
Political analysts and even Indian officials themselves describe India and China’s complex relationship as “frenemies.”
“In Hollywood there is a term, which has become quite popular. And that, I think, is called frenemies,” said India’s permanent representative to the United Nations, Syed Akbaruddin, during a recent talk in Washington. “That’s what we have with China. We engaged with them, we compete with them. In some areas we work with them together and in some areas we agree to disagree and move on.”
This could be true for any number of countries but for India and China, their relationship seems especially slippery.
They fought a short but intense war in the 1960s, supported insurgencies in each other’s backyards, clashed over very different ideologies, and sparred over trade deficits.
At the same time, India and China often bend over backward to look like they are getting along, sticking together at international conferences on climate change and holding high-level meetings with the cheery goal of doing nothing more than deepening their friendship.
Mr. Modi and Mr. Xi are to meet in Wuhan for two days. Both sides have characterized this as a purely friendly get-together, with no big agreement to sign and no set agenda other than to improve the relationship.
But analysts still expect Mr. Modi to tackle tough topics like India’s growing trade deficit, pushing China to make it easier for Indian companies to export to China. That would play well here in India, where Mr. Modi has promised to sustain a wave of job growth.
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Mr. Modi’s hope, analysts say, is that the interaction this week will include some quality leader-to-leader time like he had with Mr. Xi during a summit meeting in India in 2014, when Mr. Modi brought Mr. Xi to his home state, Gujarat, where they sat together on a swing.
Still, analysts say Mr. Modi needs Mr. Xi more than Mr. Xi needs Mr. Modi.
“India is no longer in a position to compete with China,” said Jonathan Holslag, a professor at the Free University of Brussels. “It has failed to bolster its national power through industrialization, as China did, yet remains too proud to replace its nonalignment strategy with a real alliance with the United States. As a result, it continues to get weaker.”
India and the United States have grown close in recent years, probably closer than they have ever been. The two nations share countless business ties and a commitment to democracy and have agreed to cooperate on nuclear activities. And President Trump has spoken of a “free and open Indo-Pacific,” which China regards as a thinly veiled attempt to recruit India’s help in containing it.
“The Chinese know that India is a critical swing state, probably the most critical swing state in the world,” said Brahma Chellaney, a professor of strategic studies at the Center for Policy Research in New Delhi. “If India would ally with the U.S. and other democratic powers, it would greatly impinge on China.”
But that may not necessarily happen, Mr. Chellaney said, because the United States itself has not stood up forcefully to China, which makes India cautious about being too closely identified as joining the anti-China camp.
“Will the U.S. really help us if China were to launch a strategic attack?” he said. “That is a question a lot of Asian countries are now asking.”
India’s style of government — highly decentralized, with nearly two dozen officially recognized languages and a noisy democracy — is anathema to China’s iron-fisted central control. In the battle for influence across the South Asia region, Mr. Modi tries to use this, emphasizing India’s tradition of tolerance and diversity.
But it does not always work, partly because of money. China has so much more, and it is pouring huge amounts into Sri Lanka, Nepal, Bangladesh and the Maldives — all South Asian countries traditionally dependent on India that are now feeling China’s pull.
As for Pakistan, India’s most direct rival, China is especially generous, recently committing to more than $50 billion in infrastructure projects there.
In 1980, India’s and China’s economies were about the same size. But in the decades since, while China has rapidly industrialized, India has struggled more. China’s economy is now about five times larger than India’s.
Indian analysts say this could be a source of cooperation, if India embraces the right attitude. China could export its surplus goods and capacity and India could get the infrastructure and cheap products its people need.
“But their economic relationship is being hampered by their political relationship,” said Mr. Joshi, the Observer Research Foundation fellow.
On the other hand, many people in India tend to look at China, and especially its military muscle, with some awe.
Subramanian Swamy, a member of Parliament and Mr. Modi’s political party, said that Indians “have one train of thought: that we shouldn’t fight with the Chinese.”