Excitable spring-wing dynamics 3: The dynamics of asynchronous actuation and emergent spring-wing oscillations

Many flapping wing insects use muscle pairs in which a stretch of the muscle causes a delayed-stretch activation (dSA) force without neural input. Delayed-stretch activation between antagonistic muscle pairs thus sets up self-excited, emergent wing oscillations without the need for a neural “clock”. Despite substantial work on the physiology and neuroscience of dSA muscles, a broader systems level understanding of the dynamics of dSA actuation are lacking. I will present our theoretical, numerical and robophysical modeling of dSA spring-wing systems to establish a parameter space of emergent dSA oscillations. We focus on two factors in dSA actuation, the time-delay τ between muscle stretch and peak force, and the amplitude of the force response, F_SA. Physiology experiments have observed a linear relationship between \tau and wingbeat period across a broad range of asynchronous insects, yet the consequences of τ are unclear. Our experiment and analysis demonstrate the importance of delay in dSA actuation with too much delay inhibiting emergent oscillations, and too little delay being impractical from physiological and dynamical limitations. Overall in this talk we will establish the rules of dSA oscillations in a model system of asynchronous spring-wing systems.