A Pair of Oscillators with Different Frequencies

Let us next consider the mutual entrainment between two oscillators which are symmetrically coupled to each other. Let a system of this kind be described by 

It is assumed that the oscillators, if uncoupled, are slightly different in nature from each other, the difference being characterized by the smallness parameter e. Thus one may put 

This implies that the difference in natural frequency is also of order e. Thus the problem becomes very similar to that of (a), and a critical condition for entrainment is expected to exist. 

The period of the unperturbed oscillator, which is actually an imaginary oscillator, is denoted by T. It is straightforward to derive coupled equations for 01 and 02 (the phases of the oscillators we are considering). They are 

The condition for mutual entrainment is more easily seen by rewriting (5.2.17 a) in terms of the phase difference y/ = y/ - y/j  

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