NONLINEAR DYNAMICS OF THE FREQUENCY LOCKING OF BARORECEPTOR AND SYMPATHETIC RHYTHMS

We used phase plane analysis to identify modes of frequency locking of the 10-Hz rhythm in sympathetic nerve discharge (SND) to the cardiac cycle in urethan-anesthetized, baroreceptor-innervated cats. Frequency locking occurred in rational ratios predicted by a generic mathematic al construct called the Farey tree. Both simple harmonic ratios (e.g., 1:3) and complex ratios (e.g., 2:5) comprised of relatively prime int egers (no common divisor) were identified under natural conditions. Fr equency locking in such ratios is attributed to forcing of the 10-Hz o scillator by pulse-synchronous baroreceptor afferent nerve activity (B NA). Ventricular pacing changed the frequency of the 10-Hz rhythm as w ell as heart rate so as to maintain or change the ratio of frequency l ocking in a predictable way. Intriguingly, frequency locking of the 10 -Hz rhythm to medullary raphe sympathoinhibitory stimuli in simple har monic ratios was accompanied by increased power in the 10-Hz band of S ND, whereas locking in complex ratios led to decreased 10-Hz power. Th ese findings raise the possibility that pulse-synchronous BNA also exe rts divergent actions on the 10-Hz rhythm depending on the ratio of fr equency locking. Augmented 10-Hz power can be attributed to the resona nt properties of oscillators that are periodically forced at the same phase in their cycle.