We describe mathematical models for legged animal locomotion, focusing on rapidly running insects and highlighting past achievements and challenges that remain.Expand

SummaryWinfree has developed mathematical models for his phase resetting experiments on biological clocks. These models lead him to ask a number of mathematical questions concerning dynamical… Expand

Mixed-mode oscillations (MMOs) are trajectories of a dynamical system in which there is an alternation between oscillations of distinct large and small amplitudes. MMOs have been observed and studied… Expand

This paper describes a previously undocumented phenomenon in dynamical systems theory; namely, the occurrence of heteroclinic cycles that are structurally stable within the space of C r vector fields… Expand

Hopf bifurcations have been studied intensively in two dimensional vector fields with one slow and one fast variable [E. Krupa and P. Eckhaus, in Asymptotic Analysis II, Lecture Notes in Math. 137, Kluwer, Dordrecht, The Netherlands, 2004, pp. 295–316].Expand