• 5087 Citations
  • 37 h-Index
1976 …2020
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Research Output 1976 2019

  • 5087 Citations
  • 37 h-Index
  • 132 Article
  • 3 Conference contribution
  • 1 Chapter
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Article
1995
8 Citations (Scopus)
Structured Populations
Population Model
Functional Differential Equations
1996
19 Citations (Scopus)

A discrete, size-structured model of microbial growth and competition in the chemostat

Smith, H., 1996, In : Journal of Mathematical Biology. 34, 7, p. 734-754 21 p.

Research output: Contribution to journalArticle

microbial competition
Chemostats
Chemostat
Nutrients
microbial growth
56 Citations (Scopus)

A parabolic system modeling microbial competition in an unmixed bio-reactor

Dung, L. & Smith, H., Sep 1 1996, In : Journal of Differential Equations. 130, 1, p. 59-91 33 p.

Research output: Contribution to journalArticle

115 Citations (Scopus)

Competitive exclusion and coexistence for competitive systems on ordered danach spaces

Hsu, S. B., Smith, H. & Waltman, P., 1996, In : Transactions of the American Mathematical Society. 348, 10, p. 4083-4094 12 p.

Research output: Contribution to journalArticle

Competitive Exclusion
Competitive System
Ordered Space
Banach spaces
Coexistence
1997
6 Citations (Scopus)

Complicated dynamics for low-dimensional strongly monotone maps

Smith, H., Dec 1997, In : Nonlinear Analysis, Theory, Methods and Applications. 30, 3, p. 1911-1914 4 p.

Research output: Contribution to journalArticle

Monotone Map
82 Citations (Scopus)
Predator prey systems
Predator-prey System
Type Systems
Nonlinear equations
Global Existence
24 Citations (Scopus)

The periodically forced Droop model for phytoplankton growth in a chemostat

Smith, H., May 1997, In : Journal of Mathematical Biology. 35, 5, p. 545-556 12 p.

Research output: Contribution to journalArticle

Chemostats
Chemostat
Phytoplankton
phytoplankton
Dilution
1998
75 Citations (Scopus)

Effects of random motility on microbial growth and competition in a flow reactor

Ballyk, M., Dung, L., Jones, D. & Smith, H., Nov 1998, In : SIAM Journal on Applied Mathematics. 59, 2, p. 573-596 24 p.

Research output: Contribution to journalArticle

Motility
Reactor
Nutrients
Partial differential equations
Uniform Persistence
1999
54 Citations (Scopus)

A model of microbial growth in a plug flow reactor with wall attachment

Ballyk, M. & Smith, H., May 1999, In : Mathematical Biosciences. 158, 2, p. 95-126 32 p.

Research output: Contribution to journalArticle

Large Intestine
Pipe flow
Fouling
Reactor
Nutrients
35 Citations (Scopus)

Dynamics of a Periodically Pulsed Bio-reactor Model

Smith, H. & Zhao, X. Q., Jul 1 1999, In : Journal of Differential Equations. 155, 2, p. 368-404 37 p.

Research output: Contribution to journalArticle

Bioreactor
Dynamical systems
Monotone Dynamical System
Uniform Persistence
Principal Eigenvalue
58 Citations (Scopus)

Perturbation of a globally stable steady state

Smith, H. & Waltman, P., 1999, In : Proceedings of the American Mathematical Society. 127, 2, p. 447-453 7 p.

Research output: Contribution to journalArticle

Dynamical systems
Perturbation
Asymptotically Stable
Dynamical system
Family
2000
16 Citations (Scopus)

Competition in a chemostat with wall attachment

Stemmons, E. D. & Smith, H., Aug 2000, In : SIAM Journal on Applied Mathematics. 61, 2, p. 567-595 29 p.

Research output: Contribution to journalArticle

Chemostats
Chemostat
Coexistence
Invasion
Scenarios
3 Citations (Scopus)

Competition in the periodic gradostat

Smith, H. & Waltman, P., Mar 2000, In : Nonlinear Analysis: Real World Applications. 1, 1, p. 177-188 12 p.

Research output: Contribution to journalArticle

156 Citations (Scopus)

Global asymptotic stability of traveling waves in delayed reaction-diffusion equations

Smith, H. & Zhao, X. Q., Feb 2000, In : SIAM Journal on Mathematical Analysis. 31, 3, p. 514-534 21 p.

Research output: Contribution to journalArticle

Liapunov Stability
Abstract Differential Equations
Supersolution
Subsolution
Squeezing
16 Citations (Scopus)

Microbial competition for nutrient and wall sites in plug flow

Jones, D. & Smith, H., May 2000, In : SIAM Journal on Applied Mathematics. 60, 5, p. 1576-1600 25 p.

Research output: Contribution to journalArticle

Nutrients
Reactor
Steady-state Solution
Mathematical models
Advection
10 Citations (Scopus)

Microbial growth in a plug flow reactor with wall adherence and cell motility

Smith, H. & Zhao, X. Q., Jan 1 2000, In : Journal of Mathematical Analysis and Applications. 241, 1, p. 134-155 22 p.

Research output: Contribution to journalArticle

Cell Motility
Reactor
16 Citations (Scopus)

Stable Periodic Orbits for a Predator-Prey Model with Delay

Cavani, M., Lizana, M. & Smith, H., Sep 15 2000, In : Journal of Mathematical Analysis and Applications. 249, 2, p. 324-339 16 p.

Research output: Contribution to journalArticle

Time Lag
Predator-prey Model
Periodic Orbits
Orbits
Unstable
2001
127 Citations (Scopus)

Chain transitivity, attractivity, and strong repellors for semidynamical systems

Hirsch, M. W., Smith, H. & Zhao, X. Q., 2001, In : Journal of Dynamics and Differential Equations. 13, 1, p. 107-131 25 p.

Research output: Contribution to journalArticle

Attractivity
Permanence
Transitivity
Uniform Persistence
Continuous Map
21 Citations (Scopus)

Competitive exclusion in a discrete-time, size-structured chemostat model

Smith, H. & Zmao, X. Q., 2001, In : Discrete and Continuous Dynamical Systems - Series B. 1, 2, p. 183-191 9 p.

Research output: Contribution to journalArticle

Chemostat Model
Competitive Exclusion
Chemostats
Chemostat
Matrix Models
166 Citations (Scopus)

Global dynamics of an seir epidemic model with vertical transmission

Li, M. Y., Smith, H. & Wang, L., 2001, In : SIAM Journal on Applied Mathematics. 62, 1, p. 58-69 12 p.

Research output: Contribution to journalArticle

Vertical Transmission
Global Dynamics
Epidemic Model
Basic Reproduction number
Endemic Equilibrium
30 Citations (Scopus)

How many species can two essential resources support?

Li, B. & Smith, H., 2001, In : SIAM Journal on Applied Mathematics. 62, 1, p. 336-366 31 p.

Research output: Contribution to journalArticle

Chemostats
Resources
Microorganisms
Nutrients
Chemostat Model
19 Citations (Scopus)

Microbial competition in reactors with wall attachment: A mathematical comparison of chemostat and plug flow models

Ballyk, M. M., Jones, D. & Smith, H., 2001, In : Microbial Ecology. 41, 3, p. 210-221 12 p.

Research output: Contribution to journalArticle

microbial competition
chemostat
Large Intestine
proctolin
Food
127 Citations (Scopus)

Robust persistence for semidynamical systems

Smith, H. & Zhao, X. Q., Aug 2001, In : Nonlinear Analysis, Theory, Methods and Applications. 47, 9, p. 6169-6179 11 p.

Research output: Contribution to journalArticle

Asymptotic stability
Persistence
Robustness
Uniform Persistence
Equilibrium Solution
30 Citations (Scopus)

Stable coexistence and bi-stability for competitive systems on ordered Banach spaces

Smith, H. & Thieme, H., Oct 10 2001, In : Journal of Differential Equations. 176, 1, p. 195-222 28 p.

Research output: Contribution to journalArticle

Ordered Banach Space
Competitive System
Bistability
Banach spaces
Set theory
2002
15 Citations (Scopus)

Bacterial wall attachment in a flow reactor

Jones, D., Kojouharov, H. V., Le, D. & Smith, H., May 2002, In : SIAM Journal on Applied Mathematics. 62, 5, p. 1728-1771 44 p.

Research output: Contribution to journalArticle

Reactor
Antimicrobial agents
Pipe flow
Fouling
Bioreactors
5 Citations (Scopus)

Strong positivity of solutions to parabolic and elliptic equations on nonsmooth domains

Le, D. & Smith, H., Nov 1 2002, In : Journal of Mathematical Analysis and Applications. 275, 1, p. 208-221 14 p.

Research output: Contribution to journalArticle

Nonsmooth Domains
Positivity
Elliptic Equations
Parabolic Equation
Weak Solution
2003
98 Citations (Scopus)

Feedback control for chemostat models

De Leenheer, P. & Smith, H., Jan 2003, In : Journal of Mathematical Biology. 46, 1, p. 48-70 23 p.

Research output: Contribution to journalArticle

Chemostat Model
Chemostats
Chemostat
Coexistence
Feedback Control
1 Citation (Scopus)

Microbial competition for nutrient in a 3D flow reactor

Jones, D., Kojouharov, H. V., Le, D. & Smith, H., Feb 2003, In : Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms. 10, 1-3, p. 57-67 11 p.

Research output: Contribution to journalArticle

Nutrients
Reactor
Reference Model
Biofilm
Biofilms
18 Citations (Scopus)

Periodic coexistence of four species competing for three essential resources

Li, B. & Smith, H., Aug 2003, In : Mathematical Biosciences. 184, 2, p. 115-135 21 p.

Research output: Contribution to journalArticle

Competing Species
Coexistence
coexistence
Resources
new species
19 Citations (Scopus)

The Freter model: A simple model of biofilm formation

Jones, D., Kojouharov, H. V., Le, D. & Smith, H., Aug 2003, In : Journal of Mathematical Biology. 47, 2, p. 137-152 16 p.

Research output: Contribution to journalArticle

Biofilm
Antimicrobial agents
Biofilms
Conceptual Model
Anti-Infective Agents
275 Citations (Scopus)

Virus dynamics: A global analysis

De Leenheer, P. & Smith, H., Mar 2003, In : SIAM Journal on Applied Mathematics. 63, 4, p. 1313-1327 15 p.

Research output: Contribution to journalArticle

Global Analysis
Viruses
Virus
Chronic Disease
Basic Reproduction number
2004
29 Citations (Scopus)

Traveling waves in a bio-reactor model

Smith, H. & Zhao, X. Q., Dec 2004, In : Nonlinear Analysis: Real World Applications. 5, 5, p. 895-909 15 p.

Research output: Contribution to journalArticle

Geometric Singular Perturbation Theory
Phase Plane Analysis
Center Manifold Theorem
Bioreactor
Parabolic Systems
2005
8 Citations (Scopus)

Biofilms and the plasmid maintenance question

Imran, M., Jones, D. & Smith, H., Feb 2005, In : Mathematical Biosciences. 193, 2, p. 183-204 22 p.

Research output: Contribution to journalArticle

Chemostats
Biofilm
Biofilms
plasmid
biofilm
75 Citations (Scopus)

Monotone maps: A review

Hirsch, M. W. & Smith, H., Apr 2005, In : Journal of Difference Equations and Applications. 11, 4-5, p. 379-398 20 p.

Research output: Contribution to journalArticle

Monotone Map
Review
2006
17 Citations (Scopus)

A resource-based model of microbial quiescence

Malik, T. & Smith, H., Aug 2006, In : Journal of Mathematical Biology. 53, 2, p. 231-252 22 p.

Research output: Contribution to journalArticle

Nutrients
Resources
Sleep
Dichotomy
Wake
13 Citations (Scopus)

Asymptotically stable equilibria for monotone semiflows

Hirsch, M. W. & Smith, H., Mar 2006, In : Discrete and Continuous Dynamical Systems. 14, 3, p. 385-398 14 p.

Research output: Contribution to journalArticle

Semiflow
Asymptotically Stable
Partial differential equations
Monotone
Kolmogorov System
8 Citations (Scopus)

Multiple limit cycles in the standard model of three species competition for three essential resources

Baer, S., Li, B. & Smith, H., Jun 2006, In : Journal of Mathematical Biology. 52, 6, p. 745-760 16 p.

Research output: Contribution to journalArticle

Chemostats
Hopf bifurcation
orbits
Orbit
Heteroclinic Cycle
40 Citations (Scopus)

Nonmonotone systems decomposable into monotone systems with negative feedback

Enciso, G. A., Smith, H. & Sontag, E. D., May 1 2006, In : Journal of Differential Equations. 224, 1, p. 205-227 23 p.

Research output: Contribution to journalArticle

Monotone Systems
Negative Feedback
Decomposable
Dynamical systems
Feedback
29 Citations (Scopus)

The discrete dynamics of monotonically decomposable maps

Smith, H., Oct 2006, In : Journal of Mathematical Biology. 53, 4, p. 747-758 12 p.

Research output: Contribution to journalArticle

Discrete Dynamics
Decomposable
Stage-structured
Structured Populations
Globally Asymptotically Stable
16 Citations (Scopus)

The pharmacodynamics of antibiotic treatment

Mudassar, I. & Smith, H., Dec 2006, In : Computational and Mathematical Methods in Medicine. 7, 4, p. 229-263 35 p.

Research output: Contribution to journalArticle

Pharmacodynamics
Antibiotics
Infection
Anti-Bacterial Agents
Nutrients
2007
23 Citations (Scopus)

Dynamics of stoichiometric bacteria-algae interactions in the epilimnion

Wang, H., Smith, H., Kuang, Y. & Elser, J., 2007, In : SIAM Journal on Applied Mathematics. 68, 2, p. 503-522 20 p.

Research output: Contribution to journalArticle

Algae
Bacteria
Nucleic acids
Bifurcation Diagram
Lakes
24 Citations (Scopus)

Global dynamics of microbial competition for two resources with internal storage

Li, B. & Smith, H., Oct 2007, In : Journal of Mathematical Biology. 55, 4, p. 481-515 35 p.

Research output: Contribution to journalArticle

microbial competition
Systems Theory
Global Dynamics
Internal
Resources
10 Citations (Scopus)

The dynamics of bacterial infection, innate immune response, and antibiotic treatment

Imran, M. & Smith, H., Jul 2007, In : Discrete and Continuous Dynamical Systems - Series B. 8, 1, p. 127-143 17 p.

Research output: Contribution to journalArticle

Immune Response
Antibiotics
Infection
Tissue
Nutrients
2008
16 Citations (Scopus)

Does dormancy increase fitness of bacterial populations in time-varying environments?

Malik, T. & Smith, H., May 2008, In : Bulletin of Mathematical Biology. 70, 4, p. 1140-1162 23 p.

Research output: Contribution to journalArticle

Varying Environment
Dormancy
dormancy
Fitness
Time-varying
13 Citations (Scopus)

Global stability for mixed monotone systems

Smith, H., Oct 2008, In : Journal of Difference Equations and Applications. 14, 10-11, p. 1159-1164 6 p.

Research output: Contribution to journalArticle

Monotone Systems
Global Stability
Convergence of numerical methods
Difference equations
Interval Order
12 Citations (Scopus)

Models of virulent phage growth with application to phage therapy

Smith, H., 2008, In : SIAM Journal on Applied Mathematics. 68, 6, p. 1717-1737 21 p.

Research output: Contribution to journalArticle

Bacteriophages
Bacteria
Therapy
Pharmacokinetics
Growth Model
10 Citations (Scopus)

Prevalent behavior of strongly order preserving semiflows

Enciso, G. A., Hirsch, M. W. & Smith, H., Mar 2008, In : Journal of Dynamics and Differential Equations. 20, 1, p. 115-132 18 p.

Research output: Contribution to journalArticle

Semiflow
Monotone Systems
Converge
Measurability
Convex Domain
Mathematical Biology
Discrete Dynamics
Decomposable
Proposition
Corollary
2009
13 Citations (Scopus)

Bacteriophage infection dynamics: Multiple host binding sites

Smith, H. & Trevino, R. T., Jan 2009, In : Mathematical Modelling of Natural Phenomena. 4, 6, p. 109-134 26 p.

Research output: Contribution to journalArticle

Bacteriophages
Binding sites
Stochastic Model
Infection
Basic Reproductive number
18 Citations (Scopus)

Lyapunov exponents and persistence in discrete dynamical systems

Salceanu, P. L. & Smith, H., Jul 2009, In : Discrete and Continuous Dynamical Systems - Series B. 12, 1, p. 187-203 17 p.

Research output: Contribution to journalArticle

Discrete Dynamical Systems
Lyapunov Exponent
Persistence
Dynamical systems
Invariant Set