Dynamical structure functions at critical bifurcations in a Bonhoeffer-van der Pol equation

Chaotic attractors at various bifurcations in a Bonhoeffer-van der Pol (BvP) equation are studied in terms of σn(q)—the variance of fluctuations of the coarse-grained local expansion rates of nearby orbits. For all the chaotic attractors of the BvP equation the σn(q) versus q plot exhibits a peak at q = qα. We show that additional peaks, however, occur only for the attractors just before and after the bifurcations such as crisis (sudden widening of a chaotic attractor), band merging and type-I intermittency.