He was a Guggenheim fellow in 1984, and was elected president of the Society for Industrial and Applied Mathematics (SIAM), serving from 1997 to 1998.

Guckenheimer's research has focused on three areas — neuroscience, algorithms for periodic orbits, and dynamics in systems with multiple time scales.

[4] Guckenheimer studies dynamical models of a small neural system, the stomatogastric ganglion of crustaceans — attempting to learn more about neuromodulation, the ways in which the rhythmic output of the STG is modified by chemical and electrical inputs.

Employing automatic differentiation, Guckenheimer has constructed a new family of algorithms that compute periodic orbits directly.

[7] He won a Leroy P. Steele Prize in 2013 for his book (coauthored with Philip Holmes), and he gave the Moser Lecture in May 2015.