• 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
351 Citations (Scopus)

Abstract functional differential equations and reaction-diffusion systems

Martin, R. H. & Smith, H., 1990, In : Transactions of the American Mathematical Society. 321, 1, p. 1-44 44 p.

Research output: Contribution to journalArticle

Abstract Differential Equations
Banach spaces
Lyapunov functions
Functional Differential Equations
Linear equations
13 Citations (Scopus)

A classification theorem for three dimensional competitive systems

Smith, H. & Waltman, P., 1987, In : Journal of Differential Equations. 70, 3, p. 325-332 8 p.

Research output: Contribution to journalArticle

Competitive System
Three-dimensional
Theorem
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
3 Citations (Scopus)

A discrete Lyapunov function for a class of linear differential equations

Smith, H., 1990, In : Pacific Journal of Mathematics. 144, 2, p. 345-360 16 p.

Research output: Contribution to journalArticle

System of Ordinary Differential Equations
Linear differential equation
Lyapunov Function
Linear Systems
Trajectory
2 Citations (Scopus)

Allelopathy of plasmid-bearing and plasmid-free organisms competing for two complementary resources in a chemostat

Bhattacharyya, J., Smith, H. & Pal, S., Mar 2012, In : Journal of Biological Dynamics. 6, 2, p. 628-644 17 p.

Research output: Contribution to journalArticle

allelopathy
chemostat
plasmid
plasmids
organisms
2 Citations (Scopus)

A mathematical model of oncolytic virotherapy with time delay

Wang, Z., Guo, Z. & Smith, H., Jan 1 2019, In : Mathematical Biosciences and Engineering. 16, 4, p. 1836-1860 25 p.

Research output: Contribution to journalArticle

Open Access
Oncolytic Virotherapy
Viruses
Virus
Time Delay
Time delay
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
8 Citations (Scopus)

A model of optimal dosing of antibiotic treatment in biofilm

Imran, M. & Smith, H., Jun 2014, In : Mathematical Biosciences and Engineering. 11, 3, p. 547-571 25 p.

Research output: Contribution to journalArticle

Biofilm
Antibiotics
Biofilms
biofilm
antibiotics
6 Citations (Scopus)

A note on disconjugacy for second order systems

Smith, H., 1980, In : Pacific Journal of Mathematics. 89, 2, p. 447-452 6 p.

Research output: Contribution to journalArticle

Disconjugacy
Second-order Systems
Non-negative
Valid
Sufficient
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

1 Citation (Scopus)

A reaction-diffusion system with time-delay modeling virus plaque formation

Smith, H. & Thieme, H., Dec 2011, In : Canadian Applied Mathematics Quarterly. 19, 4, p. 385-399 15 p.

Research output: Contribution to journalArticle

Reaction-diffusion System
Viruses
Virus
Time Delay
Time delay
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
24 Citations (Scopus)
Uniform Persistence
Structured Populations
Global Attractor
Population Model
Functional Differential Equations
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
12 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
9 Citations (Scopus)

A uniqueness theorem for flxedp oints

Smith, H. & Stuart, C. A., 1980, In : Proceedings of the American Mathematical Society. 79, 2, p. 237-240 4 p.

Research output: Contribution to journalArticle

Banach spaces
Uniqueness Theorem
Fixed point
Completely Continuous
Eigenvalue
11 Citations (Scopus)

Bacterial competition in serial transfer culture

Smith, H., Feb 2011, In : Mathematical Biosciences. 229, 2, p. 149-159 11 p.

Research output: Contribution to journalArticle

Chemostats
Growth
Nutrients
Dilution
Mathematical models
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)

Bacteriophage and Bacteria in a Flow Reactor

Jones, D. & Smith, H., Oct 2011, In : Bulletin of Mathematical Biology. 73, 10, p. 2357-2383 27 p.

Research output: Contribution to journalArticle

Bacteriophages
bacteriophage
bacteriophages
Bacteria
Reactor
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
7 Citations (Scopus)

Bacteriophage-resistant and bacteriophage-sensitive Bacteria in a Chemostat

Han, Z. & Smith, H., Oct 2012, In : Mathematical Biosciences and Engineering. 9, 4, p. 737-765 29 p.

Research output: Contribution to journalArticle

Chemostats
Chemostat
Bacteriophages
bacteriophages
Bacteria
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
2 Citations (Scopus)

Bounded oscillation in a class of functional differential equations

Smith, H., 1976, In : Journal of Mathematical Analysis and Applications. 56, 1, p. 223-232 10 p.

Research output: Contribution to journalArticle

Functional Differential Equations
Differential equations
Oscillation
Class
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
8 Citations (Scopus)

Chemostats and epidemics: Competition for nutrients/hosts

Smith, H. & Thieme, H., Oct 2013, In : Mathematical Biosciences and Engineering. 10, 5-6, p. 1635-1650 16 p.

Research output: Contribution to journalArticle

Chemostats
Chemostat
Nutrients
Functional Response
Basic Reproduction Number
1 Citation (Scopus)

Competing subcommunities of mutualists

Smith, H., 1989, In : Computers and Mathematics with Applications. 18, 10-11, p. 949-957 9 p.

Research output: Contribution to journalArticle

Convergence to Equilibrium
Ecosystem
Persistence
Ecosystems
Time Delay
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
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
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
1 Citation (Scopus)

Competition in the Chemostat with Time-Dependent Differential Removal Rates

Fan, G., Smith, H. & Thieme, H., Mar 1 2017, In : Vietnam Journal of Mathematics. 45, 1-2, p. 153-178 26 p.

Research output: Contribution to journalArticle

Chemostat
Functional Response
Die
17 Citations (Scopus)

Competition in the gradostat: the role of the communication rate

Smith, H. & Tang, B., Apr 1989, In : Journal of Mathematical Biology. 27, 2, p. 139-165 27 p.

Research output: Contribution to journalArticle

Microorganisms
Nutrients
Vessel
Chemostats
microorganisms
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

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
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
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
10 Citations (Scopus)
Lotka-Volterra
Delay Systems
Type Systems
Instantaneous
Negative Feedback
12 Citations (Scopus)
Chemical activation
Neural networks
149 Citations (Scopus)

Cooperative systems of differential equations with concave nonlinearities

Smith, H., 1986, In : Nonlinear Analysis. 10, 10, p. 1037-1052 16 p.

Research output: Contribution to journalArticle

Cooperative Systems
System of Differential Equations
Differential equations
Nonlinearity
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
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
22 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

Dynamics of virus and immune response in multi-epitope network

Browne, C. J. & Smith, H., Feb 23 2018, (Accepted/In press) In : Journal of Mathematical Biology. p. 1-38 38 p.

Research output: Contribution to journalArticle

Epitopes
Immune Response
Viruses
epitopes
Virus
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
2 Citations (Scopus)
Equilibrium Distribution
Singular Perturbation
Vessel
mathematical models
biogeography
8 Citations (Scopus)
Structured Populations
Population Model
Functional Differential Equations
15 Citations (Scopus)
Global Solution
Existence and Uniqueness
Model
Cell Migration
Similarity Solution
Second-order Ordinary Differential Equations
Existence and Uniqueness of Solutions
Neumann Boundary Conditions
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
32 Citations (Scopus)

Fixed point techniques in a cone with applications

Gatica, J. A. & Smith, H., Nov 1 1977, In : Journal of Mathematical Analysis and Applications. 61, 1, p. 58-71 14 p.

Research output: Contribution to journalArticle

Banach spaces
Ordinary differential equations
Boundary value problems
Integral equations
Mathematical operators
3 Citations (Scopus)

Fredholm alternatives for nonlinear differential equations

Schmitt, K. & Smith, H., Sep 1982, In : Rocky Mountain Journal of Mathematics. 12, 4, p. 817-841 25 p.

Research output: Contribution to journalArticle

Fredholm Alternative
Nonlinear Differential Equations