Restoring Coordination to Systems of Nonidentical Oscillators Through Third Party Pacing

The Haken-Kelso-Bunz (HKB) model describes bistable rhythmic coordination between biological systems, capturing a wide range of empirical phenomena in brain and behavioral dynamics. The model has recently been generalized to systems of many oscillators, allowing for a quantitative study of how the dynamics of two coupled oscillators is affected by their "social environment," i.e., by a larger system of oscillators in which both are embedded. In previous work, we studied triads of identical oscillators and showed that bistability can be restored to a monostable dyad by coupling it to a third oscillator. Here, we generalize to triads of nonidentical oscillators with different natural frequencies. We show that a pair of such oscillators, whose frequency difference would cause their dynamics in isolation to be only monostable, can exhibit bistable dynamics when both are coupled to a third oscillator having an intermediate natural frequency. We discuss some applications of this work to social and neuroscience, including gerontology and healthy aging, as well as neurostimulation and the treatment of brain-based diseases, where our findings suggest intervention strategies for promoting coordination between heterogeneous components situated in larger social environments.