• 867 Citations
  • 17 h-Index
19962019

Research output per year

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Research Output

  • 867 Citations
  • 17 h-Index
  • 42 Article
  • 2 Chapter
  • 2 Conference article
1996

On noninvertible mappings of the plane: Eruptions

Billings, L. & Curry, J. H., 1 Jan 1996, In : Chaos. 6, 2, p. 108-120 13 p.

Research output: Contribution to journalArticle

15 Scopus citations
1997

Lyapunov exponents, singularities, and a riddling bifurcation

Billings, L., Curry, J. H. & Phipps, E., 1 Jan 1997, In : Physical Review Letters. 79, 6, p. 1018-1021 4 p.

Research output: Contribution to journalArticle

17 Scopus citations
1998

Symmetric functions and exact Lyapunov exponents

Billings, L., Curry, J. H. & Phipps, E., 1 Jan 1998, In : Physica D: Nonlinear Phenomena. 121, 1-2, p. 44-64 21 p.

Research output: Contribution to journalArticle

2 Scopus citations
2000

Bi-instability and the global role of unstable resonant orbits in a driven laser

Carr, T. W., Billings, L., Schwartz, I. B. & Triandaf, I., 1 Dec 2000, In : Physica D: Nonlinear Phenomena. 147, 1-2, p. 59-82 24 p.

Research output: Contribution to journalArticle

37 Scopus citations
2001

Dynamic and geometric analysis of short time series: A new comparative approach to cell-based biosensors

Billings, L., Schwartz, I. B., Pancrazio, J. J. & Schnur, J. M., 23 Jul 2001, In : Physics Letters, Section A: General, Atomic and Solid State Physics. 286, 2-3, p. 217-224 8 p.

Research output: Contribution to journalArticle

3 Scopus citations

Methods for short time series analysis of cell-based biosensor data

Schwartz, I. B., Billings, L., Pancrazio, J. J. & Schnur, J. M., 17 Sep 2001, In : Biosensors and Bioelectronics. 16, 7-8, p. 503-512 10 p.

Research output: Contribution to journalArticle

5 Scopus citations

Probability density functions of some skew tent maps

Billings, L. & Bollt, E. M., 2 Jan 2001, In : Chaos, Solitons and Fractals. 12, 2, p. 365-376 12 p.

Research output: Contribution to journalArticle

34 Scopus citations
2002

A manifold independent approach to understanding transport in stochastic dynamical systems

Bollt, E. M., Billings, L. & Schwartz, I. B., 15 Dec 2002, In : Physica D: Nonlinear Phenomena. 173, 3-4, p. 153-177 25 p.

Research output: Contribution to journalArticle

28 Scopus citations

A unified prediction of computer virus spread in connected networks

Billings, L., Spears, W. M. & Schwartz, I. B., 13 May 2002, In : Physics Letters, Section A: General, Atomic and Solid State Physics. 297, 3-4, p. 261-266 6 p.

Research output: Contribution to journalArticle

70 Scopus citations

Exciting chaos with noise: Unexpected dynamics in epidemic outbreaks

Billings, L. & Schwartz, I. B., 1 Jan 2002, In : Journal of Mathematical Biology. 44, 1, p. 31-48 18 p.

Research output: Contribution to journalArticle

55 Scopus citations

Phase-space transport of stochastic chaos in population dynamics of virus spread

Billings, L., Bollt, E. M. & Schwartz, I. B., 10 Jun 2002, In : Physical Review Letters. 88, 23, p. 2341011-2341014 4 p., 234101.

Research output: Contribution to journalArticle

45 Scopus citations

Transition to Chaos in Continuous-Time Random Dynamical Systems

Liu, Z., Billings, L., Schwartz, I. B. & Lai, Y. C., 25 Mar 2002, In : Physical Review Letters. 88, 12, p. 1241011-1241014 4 p., 124101.

Research output: Contribution to journalArticle

24 Scopus citations
2003

Noise-induced unstable dimension variability and transition to chaos in random dynamical systems

Lai, Y. C., Liu, Z., Billings, L. & Schwartz, I. B., 1 Feb 2003, In : Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 67, 2, p. 262101-2621017 1 p., 026210.

Research output: Contribution to journalArticle

35 Scopus citations
2004

Dynamical epidemic suppression using stochastic prediction and control

Schwartz, I. B., Billings, L. & Bollt, E. M., 1 Oct 2004, In : Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 70, 4 2, p. 046220-1-046220-7 046220.

Research output: Contribution to journalArticle

17 Scopus citations

Global manifold control in a driven laser: Sustaining chaos and regular dynamics

Meucci, R., Cinotti, D., Allaria, E., Billings, L., Triandaf, I., Morgan, D. & Schwartz, I. B., 15 Feb 2004, In : Physica D: Nonlinear Phenomena. 189, 1-2, p. 70-80 11 p.

Research output: Contribution to journalArticle

20 Scopus citations

Multi-scale continuum mechanics: From global bifurcations to noise induced high-dimensional chaos

Schwartz, I. B., Morgan, D. S., Billings, L. & Lai, Y. C., Jun 2004, In : Chaos. 14, 2, p. 373-386 14 p.

Research output: Contribution to journalArticle

9 Scopus citations

Stochastic bifurcation in a driven laser system: Experiment and theory

Billings, L., Schwartz, I. B., Morgan, D. S., Bollt, E. M., Meucci, R. & Allaria, E., 1 Aug 2004, In : Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 70, 2 2, p. 026220-1-026220-10 026220.

Research output: Contribution to journalArticle

14 Scopus citations

Stochastic epidemic outbreaks: Why epidemics are like lasers

Schwartz, I. B. & Billings, L., 13 Sep 2004, In : Proceedings of SPIE - The International Society for Optical Engineering. 5471, p. 266-279 14 p.

Research output: Contribution to journalConference article

2 Scopus citations
2005

Chaotic desynchronization of multistrain diseases

Schwartz, I. B., Shaw, L. B., Cummings, D. A. T., Billings, L., Mccrary, M. & Burke, D. S., 1 Dec 2005, In : Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 72, 6, 066201.

Research output: Contribution to journalArticle

36 Scopus citations

Direct characterization of chaotic and stochastic dynamics in a population model with strong periodicity

Tung, W. W., Qi, Y., Gao, J. B., Cao, Y. & Billings, L., 1 Apr 2005, In : Chaos, Solitons and Fractals. 24, 2, p. 645-652 8 p.

Research output: Contribution to journalArticle

6 Scopus citations

Dynamic effects of antibody-dependent enhancement on the fitness of viruses

Cummings, D. A. T., Schwartz, I. B., Billings, L., Shaw, L. B. & Burke, D. S., 18 Oct 2005, In : Proceedings of the National Academy of Sciences of the United States of America. 102, 42, p. 15259-15264 6 p.

Research output: Contribution to journalArticle

Open Access
110 Scopus citations

Noise induced dimension changing bifurcations

Schwartz, I. B., Billings, L., Morgan, D. S. & Lai, Y. C., 12 Dec 2005, In : Proceedings of SPIE - The International Society for Optical Engineering. 5845, p. 245-255 11 p., 35.

Research output: Contribution to journalConference article

The effect of vaccinations in an immigrant model

Piccolo, C. & Billings, L., 1 Aug 2005, In : Mathematical and Computer Modelling. 42, 3-4, p. 291-299 9 p.

Research output: Contribution to journalArticle

Open Access
16 Scopus citations
2007

Instabilities in multiserotype disease models with antibody-dependent enhancement

Billings, L., Schwartz, I. B., Shaw, L. B., McCrary, M., Burke, D. S. & Cummings, D. A. T., 7 May 2007, In : Journal of Theoretical Biology. 246, 1, p. 18-27 10 p.

Research output: Contribution to journalArticle

36 Scopus citations

Using dimension reduction to improve outbreak predictability of multistrain diseases

Shaw, L. B., Billings, L. & Schwartz, I. B., 1 Jul 2007, In : Journal of Mathematical Biology. 55, 1, p. 1-19 19 p.

Research output: Contribution to journalArticle

12 Scopus citations
2008

Identifying almost invariant sets in stochastic dynamical systems

Billings, L. & Schwartz, I. B., 2008, In : Chaos. 18, 2, 023122.

Research output: Contribution to journalArticle

18 Scopus citations

The dynamics of antibody dependent enhancement in multi-strain diseases with vaccination

Billings, L., Schwartz, I. B. & Shaw, L. B., 1 Jan 2008, Frontiers of Applied and Computational Mathematics: New Jersey Institute of Technology, USA, 19 - 21 May 2008. World Scientific Publishing Co., p. 56-63 8 p.

Research output: Chapter in Book/Report/Conference proceedingChapter

Thermally activated switching in the presence of non-Gaussian noise

Billings, L., Dykman, M. I. & Schwartz, I. B., 24 Nov 2008, In : Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 78, 5, 051122.

Research output: Contribution to journalArticle

14 Scopus citations

Vaccinations in disease models with antibody-dependent enhancement

Billings, L., Fiorillo, A. & Schwartz, I. B., 1 Feb 2008, In : Mathematical Biosciences. 211, 2, p. 265-281 17 p.

Research output: Contribution to journalArticle

18 Scopus citations
2009

Accurate noise projection for reduced stochastic epidemic models

Forgoston, E., Billings, L. & Schwartz, I. B., 2009, In : Chaos. 19, 4, 043110.

Research output: Contribution to journalArticle

17 Scopus citations

Predicting extinction rates in stochastic epidemic models

Schwartz, I. B., Billings, L., Dykman, M. & Landsman, A., 6 May 2009, In : Journal of Statistical Mechanics: Theory and Experiment. 2009, 1, P01005.

Research output: Contribution to journalArticle

38 Scopus citations

When to spray: A time-scale calculus approach to controlling the impact of west nile virus

Thomas, D., Weedermann, M., Billings, L., Hoffacker, J. & Washington-Allen, R. A., Dec 2009, In : Ecology and Society. 14, 2

Research output: Contribution to journalArticle

Open Access
11 Scopus citations
2010

Effective vaccination policies

Shaw, L., Spears, W., Billings, L. & Maxim, P., 1 Oct 2010, In : Information Sciences. 180, 19, p. 3728-3744 17 p.

Research output: Contribution to journalArticle

5 Scopus citations

Switching exponent scaling near bifurcation points for non-gaussian noise

Billings, L., Schwartz, I. B., McCrary, M., Korotkov, A. N. & Dykman, M. I., 7 Apr 2010, In : Physical Review Letters. 104, 14, 140601.

Research output: Contribution to journalArticle

17 Scopus citations
2011

Set-based corral control in stochastic dynamical systems: Making almost invariant sets more invariant

Forgoston, E., Billings, L., Yecko, P. & Schwartz, I. B., 4 Feb 2011, In : Chaos. 21, 1, 013116.

Research output: Contribution to journalArticle

18 Scopus citations
2012

Disease persistence in epidemiological models: The interplay between vaccination and migration

Burton, J., Billings, L., Cummings, D. A. T. & Schwartz, I. B., 1 Sep 2012, In : Mathematical Biosciences. 239, 1, p. 91-96 6 p.

Research output: Contribution to journalArticle

8 Scopus citations
2013

Intervention-Based Stochastic Disease Eradication

Billings, L., Mier-y-Teran-Romero, L., Lindley, B. & Schwartz, I. B., 5 Aug 2013, In : PLoS ONE. 8, 8, e70211.

Research output: Contribution to journalArticle

Open Access
12 Scopus citations

Succeeding in undergraduate student research: A few helpful hints for advisors

Billings, L., 1 Aug 2013, In : PRIMUS. 23, 9, p. 798-804 7 p.

Research output: Contribution to journalArticle

2 Scopus citations
2014

Analysis and Control of Pre-extinction Dynamics in Stochastic Populations

Nieddu, G., Billings, L. & Forgoston, E., 6 Dec 2014, In : Bulletin of Mathematical Biology. 76, 12, p. 3122-3137 16 p.

Research output: Contribution to journalArticle

6 Scopus citations
2015

Herbivory and stoichiometric feedbacks to primary production

Krumins, J. A., Krumins, V., Forgoston, E., Billings, L. & Van Der Putten, W. H., 22 Jun 2015, In : PLoS ONE. 10, 6, e0129775.

Research output: Contribution to journalArticle

8 Scopus citations

Noise-induced switching and extinction in systems with delay

Schwartz, I. B., Billings, L., Carr, T. W. & Dykman, M. I., 26 Jan 2015, In : Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 91, 1, 012139.

Research output: Contribution to journalArticle

Open Access
9 Scopus citations
2016

Computing the optimal path in stochastic dynamical systems CHAOS 26, 083101 (2016)

Bauver, M., Forgoston, E. & Billings, L., 1 Aug 2016, In : Chaos. 26, 8, 083101.

Research output: Contribution to journalArticle

4 Scopus citations
2017

Adoption of switchgrass cultivation for biofuel under uncertainty: A discrete-time modeling approach

Burli, P., Forgoston, E., Lal, P., Billings, L. & Wolde, B., 1 Jan 2017, In : Biomass and Bioenergy. 105, p. 107-115 9 p.

Research output: Contribution to journalArticle

Extinction pathways and outbreak vulnerability in a stochastic Ebola model

Nieddu, G. T., Billings, L., Kaufman, J. H., Forgoston, E. & Bianco, S., 1 Feb 2017, In : Journal of the Royal Society Interface. 14, 127, 20160847.

Research output: Contribution to journalArticle

10 Scopus citations
2018

Seasonal forcing in stochastic epidemiology models

Billings, L. & Forgoston, E., 1 Jun 2018, In : Ricerche di Matematica. 67, 1, p. 27-47 21 p.

Research output: Contribution to journalArticle

4 Scopus citations
2019

Model reduction in stochastic environments

Forgoston, E., Billings, L. & Schwartz, I. B., 1 Jan 2019, Interdisciplinary Mathematical Sciences. World Scientific Publishing Co. Pte. Ltd., p. 37-61 25 p. (Interdisciplinary Mathematical Sciences; vol. 20).

Research output: Chapter in Book/Report/Conference proceedingChapter