Distinct forms of resonant optimality within insect indirect flight motors

Insect flight motors are extraordinary natural structures that operate efficiently at high frequencies. Structural resonance is thought to play a role in ensuring efficient motor operation, but the details of this role are elusive. While the efficiency benefits associated with resonance may be significant, a range of counterintuitive behaviours are observed. In particular, the relationship between insect wingbeat frequencies and thoracic natural frequencies is uncertain, with insects showing wingbeat frequency modulation over both short and long time scales. Here, we offer new explanations for this modulation. We show how, in linear and nonlinear models of an indirect flight motor, resonance is not a unitary state at a single frequency, but a complex cluster of distinct and mutually exclusive states, each representing a different form of resonant optimality. Additionally, by characterizing the relationship between resonance and the state of negative work absorption within the motor, we demonstrate how near-perfect resonant energetic optimality can be maintained over significant wingbeat frequency ranges. Our analysis leads to a new conceptual model of flight motor operation: one in which insects are not energetically restricted to a precise wingbeat frequency, but instead are robust to changes in thoracic and environmental properties-an illustration of the extraordinary robustness of these natural motors.