Classes:
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My Research Interests: Deterministic and Stochastic Dynamical Systems, Theory and Applications of Chaos, Ordinary Differential Equations, and Mathematical Biology and Epidemiology;
Publications
Eric Forgoston, Lora Billings, Philip Yecko, and Ira B. Schwartz, "Set-based corral control in stochastic dynamical systems: Making almost invariant sets more invariant," CHAOS 21(1), 013116 (2011).
Lucas Shaw, William M. Spears, Lora Billings, and Paul M. Maxim, "Effective Vaccination Policies," Information Sciences 180, 19 (2010), 3728-3744. PDF
Jonathan Ballone (advisor Lora Billings), "Early die out events in SIR epidemic models," Rose Hulman Undergraduate Math Journal, Vol. 11, Issue 1 (2010). Link
Lora Billings, Mark I. Dykman, Marie McCrary, A. N. Korotkov, and Ira B. Schwartz, "Switching barrier scaling near bifurcation points for non-Gaussian noise," Physical Review Letters 104(14), 140601 (2010).
Eric Forgoston, Lora Billings, and Ira B. Schwartz, "Accurate Time Series Prediction in Reduced Stochastic Epidemic Models," Chaos 19, 043110 (2009). Abstract, PDF
Diana Thomas, Marion Weedermann, Lora Billings, Joan Hoffacker,
Robert Washington-Allen, "When to Spray: A Time Scale Calculus Approach to Controlling the Impact of West Nile Virus," Ecology and Society 14 (2009) article no. 21. Abstract
Ira B. Schwartz, Lora Billings, Mark I. Dykman, and Alexandra Landsman, "Predicting extinction rates in stochastic epidemic models" Journal of Statistical Mechanics: Theory and Experiment (2009) P01005. PDF
Lora Billings, Ira B. Schwartz, and Mark I. Dykman, "Thermally activated switching in the presence of non-Gaussian noise," Physical Review E 78 (2008) 051122. PDF
Lora Billings and Ira B. Schwartz, "Identifying almost invariant sets in stochastic dynamical systems," CHAOS 18, 023122 (2008). PDF
Lora Billings, Ira B. Schwartz, and Leah B. Shaw, "The Dynamics of Antibody Dependent Enhancement in Multi-Strain Diseases with Vaccination," Proceedings from Frontiers in Applied and Computational Mathematics 2008, New Jersey Institute of Technology, World Scientific.
Lora Billings, Amy Fiorillo, and Ira B. Schwartz, "Vaccinations in disease models with antibody-dependent enhancement," Mathematical Biosciences, 211/2 (2008) 265-281. PDF
Leah B. Shaw, Lora Billings, and Ira B. Schwartz, "Using dimension reduction to improve outbreak predictability of multistrain diseases," Journal of Mathematical Biology, 55 (2007) 1-19. PDF
Lora Billings, Ira B. Schwartz, Leah B. Shaw, Marie McCrary, Donald S. Burke and Derek A.T. Cummings, "Instabilities in multiserotype disease models with antibody-dependent enhancement," Journal of Theoretical Biology, 246 (2007) 18-27.
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Ira B. Schwartz and Lora Billings, "Fluctuation Induced Almost Invariant Sets," Naval Research Laboratory Memo Report NRL/MR/6790--0609012 (2006).
D.A.T. Cummings, I. B. Schwartz, L. Billings, L. B. Shaw, and D. S. Burke, "Dynamic Effects Of Antibody Dependent Enhancement On The Fitness Of Viruses," Proceedings of the National Academy of Sciences 102 (2005) 15259-15264.
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I. B. Schwartz, L. B. Shaw, D.A.T. Cummings, L. Billings, M. McCrary, and D. Burke, "Chaotic desynchronization of multi-strain diseases," Physical Review E 72, 066201 (2005). PDF
Carmen Piccolo and Lora Billings, "The Effect of Vaccinations in an Immigrant Model," Mathematical and Computer Modelling 42 (2005) pp. 291-299.PDF
I. B. Schwartz, L. Billings, D. S. Morgan, and Y.-C. Lai, "Noise induced dimension changing bifurcations," Proceedings from SPIE: Noise in Complex Systems and Stochastic Dynamics (2005). PDF
W.-w. Tung, Y. Qi, J.B. Gao, Y. Cao, L. Billings, "Direct characterization of chaotic and stochastic dynamics in a population model with strong periodicity," Chaos, Solitons, and Fractals, 24 (2005) pp. 645-652. PDF
I.B. Schwartz, L. Billings, and E.M. Bollt, "Dynamical epidemic suppression using stochastic prediction and control," Physical Review E 70, 046220 (2004). PDF
L. Billings, I.B. Schwartz, D.S. Morgan, E.M. Bollt, R. Meucci, and E. Allaria, "Stochastic bifurcation in a driven laser system: Experiment and theory," Physical Review E 70 026220 (2004). PDF
I. B. Schwartz and L. Billings, "Stochastic Epidemic Outbreaks: Why Epidemics Are Like Lasers," Proceedings from SPIE: Noise in Complex Systems and Stochastic Dynamics 5471 (2004) pp. 266-279. PDF
I. B. Schwartz, D. S. Morgan, L. Billings, and Y.-C. Lai, "Multi-scale continuum mechanics: From global bifurcations to noise induced high dimensional chaos," CHAOS 14:2 (2004) pp. 373-386. PDF
R. Meucci, D. Cinotti, E. Allaria, L. Billings, I. Triandaf, D. Morgan, and I.B. Schwartz, "Global manifold control in a driven laser: sustaining chaos and regular dynamics," Physica D, 189:1-2 (2004) pp. 70-80. PDF
L. Billings, E. M. Bollt, D. S. Morgan, and I. B. Schwartz, "Stochastic global bifurcation in perturbed Hamiltonian systems," Discrete and Continuous Dynamical Systems, Proceedings of the Fourth International Conference on Dynamical Systems and Differential Equations, May 24-27, 2002, Wilmington, NC, supplemental volume, 123-132 (2003). PDF
Ira Schwartz, Lora Billings, David Hollt, Anne Kusterbeck, and Ioana Triandaf, "Chemical and biological sensing -- Modeling and analysis from the real world," to be included as a chapter of the book "Mathematical and Modeling Approaches in Homeland Security," to be published in SIAM's series Frontiers in Applied Mathematics, co-edited by Tom Banks and Carlos Castillo-Chavez (2003).
Y.-C. Lai, Z. Liu, L. Billings, and I. B. Schwartz, "Noise-induced unstable dimension variability and transition to chaos in random dynamical systems," Physical Review E 67 (2003), art. no. 026210. PDF
E. M. Bollt, L. Billings, and I. B. Schwartz, "A manifold independent approach to understanding transport in stochastic dynamical systems," Physica D 173 (2002), pp. 153-177. PDF To see a movie of the PDF for the MSI model as the standard deviation of the noise is increased, click here
L. Billings, E. M. Bollt, and I. B. Schwartz, "Phase-Space Transport of Stochastic Chaos in Population Dynamics of Virus Spread," Physical Review Letters 88 (2002), art. no. 234101. PDF
L. Billings, W. M. Spears, and I. B. Schwartz, "A Unified Prediction of Computer Virus Spread in Connected Networks," Physics Letters A, 297 (2002), pp. 261-266. PDF
Z. Liu, Y.-C. Lai, L. Billings, and I. B. Schwartz, "Transition to chaos in continuous-time random dynamical systems," Physical Review Letters 88 (2002), art. no. 124101. PDF
L. Billings and I. B. Schwartz, "Exciting chaos with noise: unexpected dynamics in epidemic outbreaks," Journal of Mathematical Biology 44 (2002), pp. 31-48. PDF
I. B. Schwartz, L. Billings, J. J. Pancrazio, and J. M. Schnur, "Methods for short time series analysis of cell-based biosensor data," Biosensors & Bioelectronics 16 (2001), pp. 503-512. PDF
L. Billings and E. M. Bollt, "Probability density functions of some skew tent maps," Chaos, Solitons and Fractals, 12 (2001), pp. 365-376. PDF
W. M. Spears, L. Billings, and I. B. Schwartz, Modeling Viral Epidemiology, Naval Research Laboratory Memo Report, NRL/MR/6700--01-8537 (2001).
L. Billings, I. B. Schwartz, J. J. Pancrazio, and J. M. Schnur, "Dynamic and geometric analysis of short time series: a new comparative approach to cell-based biosensors," Physics Letters A, 286 (2001), pp. 217-224.
T. W. 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 (2000), pp. 59-82. PDF
L. Billings, J. H. Curry and V. Robins, "Chaos in Relaxed Newton's Method: The Quadratic Case," Contemporary Mathematics, 252 (1999), pp. 63-70. PDF
L. Billings, J. H. Curry and E. Phipps, "Symmetric Functions and Exact Lyapunov Exponents," Physica D, 121 (1998), pp. 44-64. PDF
L. Billings, J. H. Curry and E. Phipps, "Lyapunov Exponents, Singularities and a Riddling Bifurcation," Physical Review Letters, 79 (1997), pp. 1018-1021. PDF
L. Billings and J. H. Curry, "On Noninvertible Mappings of the Plane: Eruptions," CHAOS, 6(1996), pp. 108-120. PDF
L. Billings and J. H. Curry, Bifurcations in a Class of Noninvertible Mappings of the Plane. Proceedings from CESA '96 IMACS Multiconference: Computational Engineering in Systems Applications held in Lille, France. 2 (1996), pp. 625-629.
