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Research Output 1996 2019

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

Model Reduction
Stochastic Systems
Stochastic systems
Duffing Oscillator
Infectious Diseases
2018
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
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

Panicum virgatum
Biofuels
biofuels
biofuel
uncertainty
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
2016
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
2015
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
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
2014
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
2013
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
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
2012
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
2011
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., 1 Jan 2011, In : Chaos. 21, 1, 013116.

Research output: Contribution to journalArticle

Stochastic Dynamical Systems
Invariant Set
dynamical systems
actuation
Dynamical systems
2010
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
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
2009
16 Citations (Scopus)

Accurate noise projection for reduced stochastic epidemic models

Forgoston, E., Billings, L. & Schwartz, I. B., 1 Jan 2009, In : Chaos. 19, 4, 043110.

Research output: Contribution to journalArticle

Stochastic Epidemic Models
Center Manifold
Stochastic models
projection
Projection
36 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
10 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., 1 Jan 2009, In : Ecology and Society. 14, 2

Research output: Contribution to journalArticle

Open Access
West Nile virus
mosquito
spray
timescale
virus
2008
17 Citations (Scopus)

Identifying almost invariant sets in stochastic dynamical systems

Billings, L. & Schwartz, I. B., 1 Jan 2008, In : Chaos. 18, 2, 023122.

Research output: Contribution to journalArticle

Stochastic Dynamical Systems
Markov processes
translating
Stochastic systems
Invariant Set

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

Vaccination
infectious diseases
antibodies
Antibody
Enhancement
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
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
2007
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)

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
2005
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
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
104 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

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

Chaos theory
chaos
Chaos
Bifurcation
routes
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
2004
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, 046220.

Research output: Contribution to journalArticle

adaptive control
stochastic processes
Adaptive Control
Stochastic Processes
retarding
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
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., 1 Jan 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
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 Jan 2004, In : Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 70, 2, 1 p.

Research output: Contribution to journalArticle

Stochastic Bifurcation
Frobenius-Perron Operator
Laser
Stochastic Perturbation
lasers
2 Citations (Scopus)

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

Bursting
fever
Laser
Population dynamics
Lasers
2003
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
2002
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
63 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
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
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
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
2001
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
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
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
2000
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
1998
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
1997
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
1996
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