China was originally settled on the Yellow river which gives extremely fertile land, making it great for massive population growth, but it is also heavily prone to flooding. This means that generally while it could sustain massive population booms, whenever the river flooded it could lead to population decreases. A lot of the other land that China controlled throughout the ages is infertile and makes the population rely on the yellow river for food production even more, massive territorial regions like the Tibetan plateau and the Xinjiang region relied almost entirely on food to be imported from the Yellow River ( latter this need would decrease after the Colombian exchange brought food that could survive colder climates and higher altitudes)
The massive increases and decreess in population could also be attributed to certain dynasties rising and falling. Because China had a huge population they also had a lot of soldiers to throw into their wars, so whenever a catastrophic event occurred it meant that it could really destroy the population. Most famously the Taiping Rebellion is still the most devastating civil war in history in terms of numbers of people killed, with sources differing between 17 and 30 million people. But other conquests can also be attributed to population changes, like the Mongol invasion, or the Manchu conquest forming the Qing dynasty that lead to a large population growth, this graph gives a much better depiction of China's growth over the centuries than the one by HYDE.
So that's just some general reasons that China's population can change so much, but I'm going to try and point out some more specific moments in this GIF. But first I want to point out how skeptical I am about the accuracy of this GIF. The big issue is how difficult it can be to precisely pin down populations, especially when going so far back in time. I wouldn't place a lot of trust in the numbers HYDE gives when going so far back as 10,000 BCE. That being said the original boom in population can most likely be attributed to implantation of rice farming around 7,000 BCE. It's suspected that rice farming began around 10,000 BCE but the oldest concrete evidence we have is from 7,000 BCE. Rice is extremely useful for growing a population as it can support about 1,000 people per square mile and it doesn't deplete the soil. Another specific boost is around 1000 BCE, which is around when the Zhou dynasty is established, which goes back to my earlier point about the rise of dynasties typically resulted in large growth in populations.
Feel free to ask any follow up questions.
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