How do speakers vibrate for a complex music?

A loudspeaker can be modeled as a linear AC motor driving a flexible membrane. The motor components (in this case, the voice coil and the cone) have a certain amount of mass, and the membrane's clamped circumference possesses compliance, and when taken together they result in a fundamental resonant frequency. When the speaker is driven by any AC waveform whose frequency components are less than or equal to that resonant frequency, the cone will produce an analog representation of the driving waveform no matter how complicated it might be.

By inserting compliance into the cone itself, in the form of circular ribs pressed into it, it is possible to extend the frequency response of the speaker above its fundamental resonance by allowing the outermost annular mass elements of the cone to decouple from the centermost elements of the cone at frequencies above the fundamental, progressively turning a 12" diameter cone into an 8" or a 6" or a 4" or a 2" cone with less mass and a higher resonant frequency. This allows the centermost portion of the cone to respond to high frequencies contained in the driving waveform, at the same time the entire cone is still responding as a single unit to frequencies at or below the (original) fundamental.

In this way, a single ribbed speaker cone can reproduce a very broad range of frequencies- all of which were contained in the driving signal- simultaneously.

Unlike an acoustic instrument like a guitar string or a triangle that emits mostly a single frequency (and a set of its harmonics) defined by its physical characteristics (shape, tension etc.), a speaker is driven by electric signal, and its motion is controlled by this signal, rather than by speaker's shape.

At each point in time the position of a speaker's membrane is basically by how much current or voltage is applied to the speaker input. This makes it possible to reproduce an arbitrary waveform containing Fourier series components up to some cutoff frequency. The different frequencies add up following the superposition principle.

There must be a limit to the complexity of the oscillations and the sound that can be produced.

Right, as the frequency increases, the speaker's response amplitude decreases, and at some frequency it becomes too small to be practically useful. This limits the complexity of sounds that can be reproduced.