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Research Output 1996 2019

  • 841 Citations
  • 17 h-Index
  • 42 Article
  • 2 Chapter
  • 2 Conference article
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Article
16 Citations (Scopus)

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

Stochastic Epidemic Models
Center Manifold
Stochastic models
projection
Projection

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

Panicum virgatum
Biofuels
biofuels
biofuel
uncertainty
28 Citations (Scopus)

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

dynamical systems
operators
characteristic equations
escape
boxes
5 Citations (Scopus)

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

Extinction
extinction
Population
Noise
Demography
66 Citations (Scopus)

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

computer viruses
extinction
predictions
epidemiology
differential equations
36 Citations (Scopus)

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

chaos
orbits
topology
lasers
saddles
36 Citations (Scopus)

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

Desynchronization
antibodies
Antibody
Enhancement
augmentation
4 Citations (Scopus)

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

Stochastic Dynamical Systems
Optimal Path
dynamical systems
Numerical methods
Dynamical systems
6 Citations (Scopus)

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

Stochastic Dynamics
Chaotic Dynamics
Population Model
Periodicity
Quasi-periodic Motion
7 Citations (Scopus)

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

Epidemiological Model
Vaccination
Persistence
Migration
vaccination
17 Citations (Scopus)

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

adaptive control
stochastic processes
Adaptive Control
Stochastic Processes
retarding
3 Citations (Scopus)

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

bioinstrumentation
spikes
spiking
cells
time series analysis
105 Citations (Scopus)

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
Antibody-Dependent Enhancement
Viruses
Dengue Virus
Dengue
Virus Diseases
5 Citations (Scopus)

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

Vaccines
Vaccination
Pathogens
Evolutionary algorithms
Vaccine
54 Citations (Scopus)

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

Chaos theory
Disease Outbreaks
Noise
Chaos
childhood
10 Citations (Scopus)

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

Ebola Hemorrhagic Fever
Zoonoses
Stochastic models
Disease Outbreaks
Viruses
20 Citations (Scopus)

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

sustaining
chaos
lasers
phase control
saddles
7 Citations (Scopus)

Herbivory and stoichiometric feedbacks to primary production

Krumins, J., 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

Herbivory
primary productivity
Nitrogen
herbivores
Feedback
17 Citations (Scopus)

Identifying almost invariant sets in stochastic dynamical systems

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

Research output: Contribution to journalArticle

Stochastic Dynamical Systems
Markov processes
translating
Stochastic systems
Invariant Set
35 Citations (Scopus)

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

Antibody-Dependent Enhancement
disease models
Antibody
Antibodies
oscillation
12 Citations (Scopus)

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
Disease Eradication
extinction
Disease control
Poisson Distribution
disease control
17 Citations (Scopus)

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

attraction
exponents
dynamical systems
5 Citations (Scopus)

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

Time series analysis
Biosensing Techniques
Biosensors
Neurons
Time series
9 Citations (Scopus)

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

continuum mechanics
Continuum mechanics
Global Bifurcation
Continuum Mechanics
Chaos theory
8 Citations (Scopus)

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
Extinction
extinction
Probable
Variational Problem
Dissipative Dynamical System
35 Citations (Scopus)

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

Random Dynamical Systems
Chaotic Attractor
dynamical systems
chaos
Chaos
15 Citations (Scopus)

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

volcanic eruptions
Singular Curve
Periodic Points
exponents
Newton methods
43 Citations (Scopus)

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

viruses
chaos
mass flow
probability density functions
cells
37 Citations (Scopus)

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

Stochastic Epidemic Models
Extinction
extinction
vaccines
Vaccine
33 Citations (Scopus)

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

Tent Map
Probability density function
Skew
Invariant
Unimodal Map
3 Citations (Scopus)

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

Epidemiology
Extinction
Forcing
Stochastic models
Optimal Path
18 Citations (Scopus)

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

Stochastic Dynamical Systems
Invariant Set
dynamical systems
actuation
Dynamical systems
13 Citations (Scopus)

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

Stochastic Bifurcation
Stochastic Perturbation
Laser
perturbation
lasers
2 Citations (Scopus)

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

Guidance
student
Line
experience
mathematics
16 Citations (Scopus)

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

exponents
scaling
random noise
logarithms
crossovers
2 Citations (Scopus)

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

intermittency
exponents
Newton methods
dynamical systems
embedding
16 Citations (Scopus)

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
Vaccination
Model
Compartmental Model
Immunity
Persistence
14 Citations (Scopus)

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

Non-Gaussian Noise
Siméon Denis Poisson
Gaussian Noise
Gaussian White Noise
random noise
24 Citations (Scopus)

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

dynamical systems
chaos
saddles
scaling laws
disturbances
12 Citations (Scopus)

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

Predictability
Dimension Reduction
Disease Outbreaks
serotypes
Center Manifold
17 Citations (Scopus)

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

Antibody-Dependent Enhancement
Vaccination
disease models
Antibody
Antibodies
11 Citations (Scopus)

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
West Nile virus
mosquito
spray
timescale
virus