What's the mathematics behind "spontaneous synchronization"?

In summary, "spontaneous synchronization" is when two or more oscillators or systems spontaneously synchronize their behavior without any external influence. Mathematics plays a role in understanding this phenomenon by modeling and analyzing the behavior of oscillators and systems. "Phase locking" is a key concept in spontaneous synchronization where the oscillators or systems reach a state with the same phase and frequency. Real-life examples include fireflies flashing in unison and neurons firing in the brain. Understanding spontaneous synchronization has practical applications in fields such as physics, biology, and engineering, including designing more efficient systems and improving communication and coordination in large networks.
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I was looking at this video, and have become quite interested:

 
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