Prof. Mintchev Co-Authors "Stability of a Family of Travelling Wave Solutions in a Feedforward Chain of Phase Oscillators"
POSTED ON: January 1, 2015
The paper concerns a chain of identical phase oscillators, each coupled to only its nearest neighbour on one side. The governing equations are
is some prescribed function of time. Each
is taken to be
is a particular “pulse” function. (The results do not depend on the exact form of these, nor the values of parameters.) The model can be regarded as describing a feedforward network of theta neurons. The authors are interested in waves that travel with an approximately uniform profile and speed. They prove (under certain hypotheses) for a doubly-infinite chain (i.e.
) that a family of such waves, each with constant speed and profile, does exist. (The family is parametrised by the wave’s temporal period.) They also prove that such a wave is stable to a large class of specified perturbations. The authors then give the results of careful numerical experiments which suggest that the hypotheses needed above are true.