• 5061 Citations
  • 37 h-Index
1976 …2020
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Research Output 1976 2019

  • 5061 Citations
  • 37 h-Index
  • 132 Article
  • 3 Conference contribution
  • 1 Chapter
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Article
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
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
273 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
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
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
165 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
123 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
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
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
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
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
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

114 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
1995
152 Citations (Scopus)

Asymptotically autonomous semiflows: Chain recurrence and lyapunov functions

Mischaikow, K., Smith, H. & Thieme, H., 1995, In : Transactions of the American Mathematical Society. 347, 5, p. 1669-1685 17 p.

Research output: Contribution to journalArticle

Chain Recurrence
Semiflow
Lyapunov functions
Lyapunov Function
Omega Limit Set
8 Citations (Scopus)
Structured Populations
Population Model
Functional Differential Equations
1994
24 Citations (Scopus)
Uniform Persistence
Structured Populations
Global Attractor
Population Model
Functional Differential Equations
49 Citations (Scopus)

Competition for a single limiting resource in continuous culture: The variable-yield model

Smith, H. & Waltman, P., Aug 1994, In : SIAM Journal on Applied Mathematics. 54, 4, p. 1113-1131 19 p.

Research output: Contribution to journalArticle

Nutrients
Limiting
Resources
Competitive Exclusion
Asymptotic Behavior of Solutions
50 Citations (Scopus)

Stable Periodic Orbits for a Class of Three Dimensional Competitive Systems

Zhu, H. R. & Smith, H., May 1994, In : Journal of Differential Equations. 110, 1, p. 143-156 14 p.

Research output: Contribution to journalArticle

Competitive System
Equilibrium Point
Periodic Orbits
Orbits
Three-dimensional
1993
10 Citations (Scopus)
Lotka-Volterra
Delay Systems
Type Systems
Instantaneous
Negative Feedback
15 Citations (Scopus)
Global Solution
Existence and Uniqueness
Model
122 Citations (Scopus)

Global Stability for Infinite Delay Lotka-Volterra Type Systems

Kuang, Y. & Smith, H., Jun 1993, In : Journal of Differential Equations. 103, 2, p. 221-246 26 p.

Research output: Contribution to journalArticle

Infinite Delay
Lotka-Volterra System
Global Stability
Type Systems
Sufficient Conditions
53 Citations (Scopus)
Structured Populations
Delay Equations
Population Model
Functional Differential Equations
Differential equations
1992
60 Citations (Scopus)

Slowly oscillating periodic solutions of autonomous state-dependent delay equations

Kuang, Y. & Smith, H., 1992, In : Nonlinear Analysis. 19, 9, p. 855-872 18 p.

Research output: Contribution to journalArticle

State-dependent Delay
Delay Equations
Periodic Solution
Oscillation
1991
22 Citations (Scopus)

Competition in an n-vessel gradostat

Smith, H., Tang, B. & Waltman, P., Oct 1991, In : SIAM Journal on Applied Mathematics. 51, 5, p. 1451-1471 21 p.

Research output: Contribution to journalArticle

Bifurcation (mathematics)
Coexistence
Vessel
Dynamical systems
Monotone Dynamical System
12 Citations (Scopus)
Chemical activation
Neural networks
2 Citations (Scopus)
Equilibrium Distribution
Singular Perturbation
Vessel
mathematical models
biogeography
17 Citations (Scopus)
Infinite Delay
Lotka-Volterra System
Global Stability
Patch
Unbounded Delay
37 Citations (Scopus)

Global stability in diffusive delay Lotka-Volterra systems

Kuangt, Y., Smith, H. & Schmitt, K., 1991, In : Differential and Integral Equations. 4, 1, p. 117-128 12 p.

Research output: Contribution to journalArticle

Lotka-Volterra System
Delay Systems
Global Asymptotic Stability
Asymptotic stability
Global Stability
112 Citations (Scopus)

Reaction-diffusion systems with time delays: Monotonicity, invariance, comparison and convergence

Martin, R. H. & Smith, H., 1991, In : Journal fur die Reine und Angewandte Mathematik. 1991, 413, p. 1-35 35 p.

Research output: Contribution to journalArticle

Invariance
Reaction-diffusion System
Monotonicity
Time Delay
Time delay
30 Citations (Scopus)

Stable periodic solutions for the hypercycle system

Hofbauer, J., Mallet-Paret, J. & Smith, H., Jul 1991, In : Journal of Dynamics and Differential Equations. 3, 3, p. 423-436 14 p.

Research output: Contribution to journalArticle

Periodic Orbits
Periodic Solution
Omega Limit Set
Reactor
Orbit
98 Citations (Scopus)

Strongly order preserving semiflows generated by functional differential equations

Smith, H. & Thieme, H., 1991, In : Journal of Differential Equations. 93, 2, p. 332-363 32 p.

Research output: Contribution to journalArticle

Differential equations
19 Citations (Scopus)

The gradostat: A model of competition along a nutrient gradient

Smith, H. & Waltman, P., Dec 1991, In : Microbial Ecology. 22, 1, p. 207-226 20 p.

Research output: Contribution to journalArticle

vessel
mathematical theory
Food
nutrient
nutrients