RESUMEN
With the use of perturbation expansions
and asymptotic matching, bursting in the three-dimensional Bonhoeffer–van
der Pol equations is shown
to be the result of the interaction of two oscillatory modes, one of small
amplitude and the other of large amplitude. The large oscillations are similar
to the relaxation oscillations found in the two-dimensional van der Pol system, but the small
oscillations have not been fully understood before. This analysis also explains
the transition in the two-dimensional system from stable equilibrium to relaxation
oscillations: the intermediate stage between the two are
the small oscillations.