Thomas W. Carr, Ph.D.
Department of Mathematics
Southern Methodist University
Dallas, TX 75275-0156
T.W. Carr, “Equivalent probability density moments determine equivalent epidemics in an SIRS model with temporary immunity,” Theoretical Population Biology, 113:47-55, 2017, doi: 10.1016/j.tpb.2016.11.001.
T.W. Carr, “An SIRS epidemic model with a rapidly decreasing probability for immunity,” IMA Journal of Applied Mathematics, 81:281-307, 2016; doi: 10.1093/imamat/hxv036.
N.H. Wasserman, C. Quint, S. Norris, T.W. Carr, “Exploring Flipped Classroom Instruction in Calculus III,” International J. Sci. and Math. Education 2015; doi: 10.1007/s10763-015-9704-8.
Schwartz, L. Billings, T.W. Carr, M.I. Dykman, “Noise Induced
Switching and Extinction in Systems with Delay”, Phys. Rev. E,
91:012139, 2015. DOI: http://dx.doi.org/10.1103/PhysRevE.91.012139.
Carr, R. Haberman, T. Erneux, “Delay-periodic solutions and their
stability using averaging in delay-differential equations, with
applications,” Physica D, 241:1527-1631, 2012. DOI:
Mitchell and T.W. Carr, “Synchronous versus asynchronous
oscillations for antigenically varying Plasmodium falciparum with
host immune response,” J. Biological Dynamics, 6:333-357, 2012.
Mitchell and T.W. Carr, “The eﬀects of state-dependent delay on
a weakly-damped nonlinear oscillator,” Phys. Rev. E, 83:046110,
J.L. Mitchell and T.W. Carr, “Oscillations in an intra-host model of Plasmodium falciparum malaria due to cross-reactive immune response,” Bull. Math. Biol., 72:590-610, 2010
M.L. Taylor and T.W. Carr, “An SIR epidemic model with partial temporary immunity modeled with delay,” J. Math. Bio. 59:841-880, 2009
David Dingli, Chetan Offord, Rae Myers, Kah-Whye Peng, Thomas W. Carr, Kresimir Josic, Stephen J. Russell, and Zeljko Bajzer, “Dynamics of multiple myeloma tumor therapy with a recombinant measles virus,” Cancer Gene Therapy, doi: 10.1038/cgt.2009.40, 2009.
Z. Bajzer, T.W. Carr, K. Josic, S.J. Russel and D. Dingli, “Modeling of cancer virotherapy with recombinant measles viruses,” J. Theoretical Biology 252:109-122, 2008.
T.W. Carr, “Coupling-induced resonance in two mutually and asymmetrically coupled oscillators.” Phys. Rev. E 73: 026207, 2008.
T.W. Carr, I.B. Schwartz, M.Y. Kim, and R. Roy, “Delayed-mutual coupling dynamics of lasers: scaling laws and resonances,” SIAM J. Dynamical Systems 5:699-725, 2006.
Carr, M.L. Taylor and I.B. Schwartz, “Negative-coupling resonances
in pump-coupled lasers,” Physica D 213:152-163 (2006).
Kim, R. Roy, J.L. Aron, T.W. Carr and I.B. Schwartz, “Scaling
behavior of laser population dynamics with time-delay coupling:
theory and experiment,” Phys, Rev. Letters, 94:088101, 2005.
Carr, “Period-locking due to delayed feedback in a laser with
saturable absorber,” Phys. Rev. E, 68:026212, 2003.
Schwartz, I. Triandaf, R. Meucci and T.W. Carr, “Open-loop
sustained chaos and control: An manifold approach,” Phys. Rev. E,
Carr, “Onset of instabilities in self-pulsing semiconductor lasers
with delayed feedback,” Euro. Phys. J. D., 19:245-255, 2002.
Carr and T. Erneux, “An analytical study of a periodically driven
laser with a saturable absorber,” Euro. Phys. J. D., 17:67-74,
Carr, T. Erneux, C. Szwaj, M. Lefranc, D. Derozier, and S.
Bielawski, “Cascade of parametric instabilities in a multimode
laser,” Phys. Rev. A, 64:053808, 2001.
Carr and T. Erneux, “Dimensionless rate equations and simple
conditions for self-pulsing in laser diodes,” IEEE J. Quantum
Electron., 37:1171-1177, 2001.
Carr, D. Pieroux, and P. Mandel, “Theory of a multimode
semiconductor laser with optical feedback,” Phys. Rev. A,
Carr, L. Billings, I.B. Schwartz, and I. Triandaf, “Bi-instability
and the global role of unstable resonant orbits in a driven laser,”
Physica D, 147:59-82, 2000.
Schwartz and T.W. Carr, “Bi-instability as a precursor to global
mixed-mode chaos,” Phys. Rev. E, 59:6658-6661, 1999.
Carr and I.B. Schwartz, “On measures of disorder in globally
coupled oscillators,” Physica D, 115:321-340, 1998.
Schwartz, T.W. Carr, and I. Triandaf, “Tracking controlled chaos:
Theoretical foundations and applications,” Chaos, 7:664-679,
Booth, T. Carr, and T. Erneux, “Near threshold bursting is delayed
by a slow passage near a limit point,” SIAM J. Appl. Math.,
Carr and I.B. Schwartz, “The role of symmetry breaking and
disorder in the control of splay-phase states in globally coupled
oscillators,” Physica D, 106:113-130, 1997.
Thornburg, M. Moller, R. Roy, T.W. Carr, R.D. Li, and T. Erneux,
“Chaos and coherence in coupled lasers,” Phys. Rev. E,
Carr and I.B. Schwartz, “Symmetry-breaking control of splay-phase
states in globally coupled oscillators,” Phys. Lett. A, 227:41-46,
Carr and I.B. Schwartz, “Subharmonic-saddle connections as a
precursor to chaos in a periodically modulated laser,” Int. J.
Bif. Chaos, 6:2047-2053, 1996.
Carr and I.B. Schwartz, “Controlling high-dimensional unstable
steady states using delay, duration and feedback,” Physica D,
96:17-25, 1996. Also appeared in Measures of Spatio-Temporal
Dynamics, ed. by A.M. Albano, P.E. Rapp, N.B. Abraham and A.
Passamante, (Elsevier Science B.V.,Amsterdam, 1996).
Carr and I.B. Schwartz, “Controlling the unstable steady state in
a multimode laser,” Phys. Rev. E, 51:5109-5111, 1995.
Carr and I.B. Schwartz, “Controlling unstable steady states using
system parameter variation and control duration,” Phys. Rev. E,
Carr and T. Erneux, “Understanding bifurcation to traveling waves
in a class-b laser using a degenerate Ginzburg-Landau equation,”
Phys. Rev. A, 50:4219-4227, 1994.
Carr and T. Erneux, “The Hopf bifurcation of the class-b multimode
laser equations,” Phys. Rev. A, 50:724-731, 1994.
Adamovsky and T.W. Carr, “Intensity to frequency conversion
technique in intensity modulated fiber optic sensing systems,”
Electronics Letters, 26:1450-1451, 1990
I.B. Schwartz, T.W. Carr, L. Billings, M. Dykman, “Noise Induced Switching in Delayed Systems,” arXiv:1207.7278 [cond-mat.stat-mech], 2012.
S.T. Elliot and T.W. Car, “Thrust sensor based nonlinear motor control for quadcopters,” in 2016 IEEE Transportation Electrification Conference and Expo (ITEC), 27-29 June 2016,
Erneux, R. Kuske, and T.W. Carr, “Mathematical studies of coupled
lasers,” in Laser Optics '95: Nonlinear Dynamics in Lasers,
2792:54-64, editors N.B. Abraham and Y.I. Knanin, (SPIE, 1996).
Carr and I.B. Schwartz, “Using the control duration to stabilize a
multimode laser,” in IEEE/LEOS '95 Conference Proceedings,
1:159-160 (IEEE, 1995).
T. Erneux, T.W. Carr, and R. Li, “Coupled laser asymptotics,” in Chaos in Optics, 2039:80-90, editor, Rajarshi Roy (SPIE, 1993).
Bajzer, T.W. Carr, D. Dingli and K. Josic, “Optimization of tumor
virotherapy with recombinant measles viruses,” in Optimization
in Medicine and Biology, editors: Gino J. Lim and Eva K Lee,
(Taylor and Francis, 2007).
I. Triandaf, I.B. Schwartz, and T.W. Carr, “Geometric control and tracking methods for nonlinear dynamic systems,” in Smart Methods in Nonlinear Vibrations and Control, editors A. Guran and D. Inman, (Prentice Hall, New Jersey, 1995).
S. Elliot and T.W. Carr, “Robust nonlinear control of a BLDC motor in quadcopter applications,” American J. Undergraduate Rearch, 13:5-14 (2016).
S.T. Elliot and T.W. Carr, "Nonlinear PID Speed Control of BLDC Motors in Quadcopter Applications," submitted to SIAM Undergraduate Research Online.