This pendulum is not a normal pendulum. This is called a compound pendulum. Two pendulums are hooked together, one attached to another. With a compound pendulum, as one pendulum swings the other one is swinging as well. As one pendulum swings, its accelerations and motions are coupled to the other pendulum.
Subsequent motions are dependent on previous motions.
Given the complex interactivity between the two pendulums, it is impossible to derive simple mathematical formulas which describe the resultant motions. There's More Chaotic motions are not limited just to compound pendulums. The earth's weather is another example of a chaotic system. The atmosphere is a single entity, but conditions are different around the world. Temperatures, air pressure and humidity are affected by local situations.