This talk will repeat the 2015 Moser Prize Lecture from the SIAM Dynamical Systems meeting.

This lecture highlights interdisciplinary interactions of dynamical systems theory. Experimental data and computer simulation have inspired mathematical discoveries, while resulting theory has made successful predictions and created new scientific perspectives. Nonlinear dynamics has unified diverse fields of science and revealed deep mathematical phenomena.

Examples involving

- One dimensional maps
- Numerical bifurcation analysis
- Multiple time scales
- Bursting and MMOs in neuroscience and chemistry
- Locomotion

are described, along with emerging areas having public impact.