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Research:

Asymptotic & perturbation methods, bifurcation theory and dynamical systems theory, applied to coupled oscillators, lasers instabilities and epidemiology.

Professor Carr's research focuses on the dynamics of physical systems modeled by nonlinear ordinary and partial differential equations. He uses local and global bifurcation theory, asymptotic analysis, and numerical simulation and continuation to study the system's behavior and parameter sensitivities. Of particular interest is the synchronization characteristics of coupled oscillators. Areas of application include laser instabilities, coupled electronic circuits and mathematical biology.

He collaborates with scientists at the U.S. Naval Research Laboratory and the Free University of Brussels, Belgium. His research has appeared in Physical Review A, Physical Review E, Physical Letters A, Chaos, Physica D, and SIAM Journal of Applied Mathematics.