In the first part of this paper, we showed that three coupled populations of
identical phase oscillators give rise to heteroclinic cycles between invariant
sets where populations show distinct frequencies. Here, we now give explicit
stability results for these heteroclinic cycles for populations consisting of
two oscillators each. In systems with four coupled phase oscillator
populations, different heteroclinic cycles can form a heteroclinic network.
While such networks cannot be asymptotically stable, the local attraction
properties of each cycle in the network can be quantified by stability indices.
We calculate these stability indices in terms of the coupling parameters
between oscillator populations. Hence, our results elucidate how oscillator
coupling influences sequential transitions along a heteroclinic network where
individual oscillator populations switch sequentially between a high and a low
frequency regime; such dynamics appear relevant for the functionality of neural
oscillators
