Multilegged running; a bump in the right direction
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Legged locomotion on land is often viewed in terms of "gaits" corresponding to repeated patterns of footfalls, suggesting an application of the mathematical theory of limit cycle oscillators. Unlike classical oscillators, the oscillators appearing in locomotion encounter rapid processes that are often modeled as non-smooth "hybrid" transitions.
In the last couple of years my collaborators and I developed some insights into the unique features of hybrid limit cycle oscillators. In particular, empirical analysis of rapid multilegged locomotion that brought us to discovery a new, fundamental form of stability unique to hybrid oscillators of these gaits.