# John Davis

Professor of Mathematics

Undergraduate Program Director

#### Professor of Mathematics

##### Education

Ph.D., Auburn University, 1998 *Phi Beta Kappa*

##### Academic Interests and Research

Ordinary and partial differential equations, interplay between discrete and continuous (hybrid) dynamical systems, nonlinear systems theory, adaptive control theory, applied mathematics.

##### Research Funding

NSF Grant EHS #0410685

Real-Time Distributed Control Networks: Dynamic Bandwidth Allocation via Adaptive Sampling, 2004-2008. $311,000

NSF Grant CMMI #0726996

Mu-Dynamics on Time Scales: Adaptive Time Domains for Dynamical Systems, 2007-2010. $143,952

##### Selected (Recent) Publications

R.J. Marks II, I.A. Gravagne, J.M. Davis, "A generalized Fourier transform and convolution on time scales," *Journal of Mathematical Analysis and Applications 340* (2008), 901-919.

J.M. Davis, I.A. Gravagne, B.J. Jackson, R.J. Marks II, A.A. Ramos,
"The Laplace transform on time scales revisited,"
*Journal of Mathematical Analysis and Applications 332* (2007), 1291-1307.

R.J. Marks II, I.A. Gravagne, J.M. Davis, and J.J. DaCunha,
"Non-regressivity in switched linear circuits and mechanical systems,"
*Mathematical and Computer Modelling 43* (2006), 1383-1392.

Q. Sheng, M. Fadag, J. Henderson, and J.M. Davis,
"An exploration of combined dynamic derivatives on time scales and their applications,"
*Nonlinear Analysis 7 *(2006), 395-413.

I.A. Gravagne, J.M. Davis, R.J. Marks II,
"How deterministic must a real-time controller be?"
*Proceedings of 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems*, (IROS 2005), Alberta, Canada, Aug. 2005, 3856-3861.

##### Research Group

Dr. Ian A. Gravagne, Associate Professor of Electrical and Computer Engineering, Baylor University

Dr. Robert J. Marks II, Distinguished Professor of Electrical and Computer Engineering, Baylor University

##### Graduate Students Directed

Alice A. Ramos, Ph.D. student currently working with me

Billy J. Jackson, Ph.D. 2007

Thesis: A General Linear Systems Theory on Time Scales: Transforms, Stability, and Control

Jeffrey J. DaCunha, Ph.D. 2004

Thesis: Lyapunov Stability and Floquet Theory for Non-autonomous Linear Dynamic Systems on Time Scales

Matthew K. Brammer, M.S. 2003

Thesis: Nonlinear Dynamics and Bifurcations in the Belousov-Zhabotinskii Reaction