# zbMATH — the first resource for mathematics

## Smith, Hal Leslie

Compute Distance To:
 Author ID: smith.hal-leslie Published as: Smith, Hal L.; Smith, H. L.; Smith, Hal; Smith, Hal Leslie Homepage: https://math.la.asu.edu/~halsmith/ External Links: MGP
 Documents Indexed: 178 Publications since 1976, including 7 Books
all top 5

#### Co-Authors

 61 single-authored 16 Thieme, Horst R. 11 Jones, Don A. 11 Kuang, Yang 11 Waltman, Paul Elvis 9 Le, Dung 8 Zhao, Xiao-Qiang 7 Hirsch, Morris W. 7 Li, Bingtuan 4 Kojouharov, Hristo V. 4 Martin, Robert H. jun. 4 Salceanu, Paul Leonard 4 Schmitt, Klaus 3 Ballyk, Mary M. 3 De Leenheer, Patrick 3 Imran, Mudassar 3 Tang, Betty K. P. 2 Enciso, Germán Andrés 2 Gatica, Juan A. 2 Hsu, Sze-Bin 2 Jin, Wen 2 Korytowski, Daniel A. 2 Malik, Tufail 2 Mallet-Paret, John Joseph 1 Allen, Edward James 1 Allen, Linda J. S. 1 Baer, Steven M. 1 Bhattacharyya, Joydeb 1 Browne, Cameron J. 1 Cavani, Mario 1 Diekmann, Odo 1 Dockery, Jack D. 1 Durrett, Richard Timothy 1 Elser, James J. 1 Fan, Guihong 1 Freedman, Herbert Irving 1 Goldstein, Myron 1 Golubitsky, Martin A. 1 Hadeler, Karl-Peter 1 Han, Zhun 1 Hsu, Szebi 1 Jäger, Willi 1 Kang, Yun 1 Klapper, Isaac 1 Korytowski, Dan A. 1 Li, Michael Yi 1 Lizana, Marcos 1 Maini, Philip Kumar 1 Martelli, Mario 1 Mischaikow, Konstantin 1 Mudassar, Imran 1 Pal, Samaresh 1 Röst, Gergely 1 Schwartz, Ira Bruce 1 Sheil-Small, Terry 1 Sontag, Eduardo D. 1 Stemmons, Eric D. 1 Stepien, Tracy L. 1 Stuart, Charles Alexander 1 Tang, Baorong 1 Trevino, R. T. 1 Wang, Hao 1 Wang, Liancheng 1 Zhao, Tao 1 Zhu, Hsiu-Rong
all top 5

#### Serials

 20 Journal of Mathematical Biology 18 SIAM Journal on Applied Mathematics 12 Journal of Differential Equations 10 Journal of Mathematical Analysis and Applications 8 Journal of Dynamics and Differential Equations 7 SIAM Journal on Mathematical Analysis 6 Rocky Mountain Journal of Mathematics 6 Discrete and Continuous Dynamical Systems. Series B 6 Nonlinear Analysis. Theory, Methods & Applications 5 Mathematical Biosciences 5 The Canadian Applied Mathematics Quarterly 4 Journal of Difference Equations and Applications 4 Discrete and Continuous Dynamical Systems 3 Bulletin of Mathematical Biology 3 Transactions of the American Mathematical Society 3 Mathematical Biosciences and Engineering 3 Journal of Biological Dynamics 2 Pacific Journal of Mathematics 2 Proceedings of the American Mathematical Society 2 Differential and Integral Equations 2 SIAM Review 2 Nonlinear Analysis. Real World Applications 1 Applicable Analysis 1 Computers & Mathematics with Applications 1 Journal of the Australian Mathematical Society, Series B 1 Bulletin of the London Mathematical Society 1 Funkcialaj Ekvacioj. Serio Internacia 1 Journal für die Reine und Angewandte Mathematik 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Quarterly of Applied Mathematics 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Journal of Mathematical Chemistry 1 Differential Equations and Dynamical Systems 1 Vietnam Journal of Mathematics 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms 1 Graduate Studies in Mathematics 1 Lecture Notes in Mathematics 1 Mathematical Surveys and Monographs 1 Texts in Applied Mathematics 1 Computational & Mathematical Methods in Medicine 1 Networks and Heterogeneous Media 1 Mathematical Modelling of Natural Phenomena
all top 5

#### Fields

 126 Biology and other natural sciences (92-XX) 108 Ordinary differential equations (34-XX) 49 Dynamical systems and ergodic theory (37-XX) 42 Partial differential equations (35-XX) 14 Operator theory (47-XX) 8 Systems theory; control (93-XX) 6 Difference and functional equations (39-XX) 5 Integral equations (45-XX) 5 Numerical analysis (65-XX) 4 General and overarching topics; collections (00-XX) 4 General topology (54-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Probability theory and stochastic processes (60-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Functional analysis (46-XX) 1 Algebraic topology (55-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

#### Citations contained in zbMATH Open

162 Publications have been cited 5,421 times in 3,522 Documents Cited by Year
Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems. Zbl 0821.34003
Smith, Hal L.
1995
The theory of the chemostat. Dynamics of microbial competition. Zbl 0860.92031
Smith, Hal L.; Waltman, Paul
1995
Abstract functional differential equations and reaction-diffusion systems. Zbl 0722.35046
Martin, R. H. jun.; Smith, H. L.
1990
An introduction to delay differential equations with applications to the life sciences. Zbl 1227.34001
Smith, Hal
2011
Virus dynamics: a global analysis. Zbl 1035.34045
De Leenheer, Patrick; Smith, Hal L.
2003
Dynamical systems and population persistence. Zbl 1214.37002
Smith, Hal L.; Thieme, Horst R.
2011
Robust persistence for semidynamical systems. Zbl 1042.37504
Smith, Hal L.; Zhao, Xiao-Qiang
2001
Planar competitive and cooperative difference equations. Zbl 0907.39004
Smith, H. L.
1998
Cooperative systems of differential equations with concave nonlinearities. Zbl 0612.34035
Smith, H. L.
1986
Global asymptotic stability of traveling waves in delayed reaction-diffusion equations. Zbl 0941.35125
Smith, Hal L.; Zhao, Xiao-Qiang
2000
Global dynamics of an SEIR epidemic model with vertical transmission. Zbl 0991.92029
Li, Michael Y.; Smith, Hal L.; Wang, Liancheng
2001
Competitive exclusion and coexistence for competitive systems on ordered Banach spaces. Zbl 0860.47033
Hsu, S. B.; Smith, H. L.; Waltman, Paul
1996
Asymptotically autonomous semiflows: Chain recurrence and Lyapunov functions. Zbl 0829.34037
Mischaikow, Konstantin; Smith, Hal; Thieme, Horst R.
1995
Systems of ordinary differential equations which generate an order preserving flow. A survey of results. Zbl 0674.34012
Smith, Hal L.
1988
Global stability for infinite delay Lotka–Volterra type systems. Zbl 0786.34077
Kuang, Y.; Smith, H. L.
1993
The Poincaré-Bendixson theorem for monotone cyclic feedback systems. Zbl 0712.34060
Mallet-Paret, John; Smith, Hal L.
1990
Monotone semiflows generated by functional differential equations. Zbl 0612.34067
Smith, Hal
1987
Monotone dynamical systems. Zbl 1094.34003
Hirsch, M. W.; Smith, Hal
2005
Chain transitivity, attractivity, and strong repellors for semidynamical systems. Zbl 1129.37306
Hirsch, Morris W.; Smith, Hal L.; Zhao, Xiao-Qiang
2001
Infinite subharmonic bifurcation in an SEIR epidemic model. Zbl 0523.92020
Schwartz, Ira B.; Smith, H. L.
1983
Reaction-diffusion systems with time delays: Monotonicity, invariance, comparison and convergence. Zbl 0709.35059
Martin, R. H. jun.; Smith, H. L.
1991
The theory of the chemostat. Dynamics of microbial competition. Reprint of the 1995 hardback ed. Zbl 1139.92029
Smith, Hal L.; Waltman, Paul
2008
Effects of random motility on microbial growth and competition in a flow reactor. Zbl 1051.92039
Ballyk, Mary; Dung, Le; Jones, Don A.; Smith, Hal L.
1999
Competitive coexistence in an oscillating chemostat. Zbl 0467.92018
Smith, Hal L.
1981
Periodic competitive differential equations and the discrete dynamics of competitive maps. Zbl 0596.34013
Smith, Hal L.
1986
Global existence of periodic solutions in a class of delayed Gause-type predator-prey systems. Zbl 0872.34047
Zhao, Tao; Kuang, Yang; Smith, H. L.
1997
Strongly order preserving semiflows generated by functional differential equations. Zbl 0735.34065
Smith, Hal L.; Thieme, Horst R.
1991
Perturbation of a globally stable steady state. Zbl 0924.58087
Smith, H. L.; Waltman, P.
1999
Periodic solutions of periodic competitive and cooperative systems. Zbl 0609.34048
Smith, Hal L.
1986
A parabolic system modeling microbial competition in an unmixed bio-reactor. Zbl 0865.35017
Le Dung; Smith, Hal L.
1996
Feedback control for chemostat models. Zbl 1015.92046
De Leenheer, Patrick; Smith, Hal
2003
Slowly oscillating periodic solutions of autonomous state-dependent delay equations. Zbl 0774.34054
Kuang, Y.; Smith, H. L.
1992
Monotone maps: a review. Zbl 1080.37016
Hirsch, M. W.; Smith, Hal
2005
Convergence for strongly order-preserving semiflows. Zbl 0739.34040
Smith, Hal L.; Thieme, Horst R.
1991
Periodic solutions of differential delay equations with threshold-type delays. Zbl 0762.34044
Smith, H. L.; Kuang, Y.
1992
On the asymptotic behavior of a class of deterministic models of cooperating species. Zbl 0607.92023
Smith, Hal L.
1986
Subharmonic bifurcation in an S-I-R epidemic model. Zbl 0578.92023
Smith, H. L.
1983
Dynamics of competition in the unstirred chemostat. Zbl 0831.92028
Hsu, S. B.; Smith, H. L.; Waltman, Paul
1994
Competing subcommunities of mutualists and a generalized Kamke theorem. Zbl 0609.92033
Smith, Hal L.
1986
Reduction of structured population models to threshold-type delay equations and functional differential equations: A case study. Zbl 0797.92024
Smith, Hal L.
1993
Multiple stable subharmonics for a periodic epidemic model. Zbl 0529.92018
Smith, H. L.
1983
Invariant curves for mappings. Zbl 0606.47056
Smith, Hal L.
1986
Quasi convergence and stability for strongly order-preserving semiflows. Zbl 0704.34054
Smith, Hal L.; Thieme, Horst R.
1990
On periodic solutions of a delay integral equation modelling epidemics. Zbl 0354.92035
Smith, H. L.
1977
Dynamics of a periodically pulsed bio-reactor model. Zbl 0930.35085
Smith, Hal L.; Zhao, Xiao-Qiang
1999
The interaction of steady state and Hopf bifurcations in a two-predator- one-prey competition model. Zbl 0489.92019
Smith, Hal L.
1982
Stable periodic orbits for a class of three dimensional competitive systems. Zbl 0802.34064
Zhu, Hsiu-Rong; Smith, Hal L.
1994
Competition for a single limiting resource in continuous culture: The variable-yield model. Zbl 0829.92020
Smith, Hal L.; Waltman, Paul
1994
Periodic orbits of competitive and cooperative systems. Zbl 0615.34027
Smith, Hal L.
1986
Monotone semiflows in scalar non-quasi-monotone functional differential equations. Zbl 0719.34123
Smith, Hal L.; Thieme, Horst R.
1990
Fixed point techniques in a cone with applications. Zbl 0435.47060
Gatica, J. A.; Smith, Hal L.
1977
Oscillations and multiple steady states in a cyclic gene model with repression. Zbl 0619.92004
Smith, Hal
1987
On eigenvalue problems for nondifferentiable mappings. Zbl 0389.34019
Schmitt, K.; Smith, H. L.
1979
Stable coexistence and bi-stability for competitive systems on ordered Banach spaces. Zbl 1064.47075
Smith, H. L.; Thieme, H. R.
2001
A model of microbial growth in a plug flow reactor with wall attachment. Zbl 0980.92034
Ballyk, Mary; Smith, Hal
1999
How many species can two essential resources support? Zbl 0992.92040
Li, Bingtuan; Smith, Hal
2001
Global stability in diffusive delay Lotka-Volterra systems. Zbl 0752.34041
Kuang, Y.; Smith, H. L.
1991
Competition in an $$n$$-vessel gradostat. Zbl 0749.92024
Smith, H. L.; Tang, Betty; Waltman, Paul
1991
The discrete dynamics of monotonically decomposable maps. Zbl 1118.65057
Smith, H. L.
2006
Positive solutions and conjugate points for systems of differential equations. Zbl 0379.34015
Schmitt, K.; Smith, H. L.
1978
Nonmonotone systems decomposable into monotone systems with negative feedback. Zbl 1103.34021
Enciso, G. A.; Smith, H. L.; Sontag, E. D.
2006
A structured population model and a related functional differential equation: Global attractors and uniform persistence. Zbl 0794.34061
Smith, Hal L.
1994
Steady states of models of microbial growth and competition with chemotaxis. Zbl 0933.35088
Le Dung; Smith, Hal L.
1999
Stable periodic solutions for the hypercycle system. Zbl 0729.34032
Hofbauer, J.; Mallet-Paret, J.; Smith, H. L.
1991
Competition in the chemostat: some remarks. Zbl 1132.92341
De Leenheer, Patrick; Li, Bingtuan; Smith, Hal L.
2003
Traveling waves in a bio-reactor model. Zbl 1079.35011
Smith, Hal L.; Zhao, Xiao-Qiang
2004
Dynamics of competition. Zbl 1002.92564
Smith, H. L.
1999
The periodically forced Droop model for phytoplankton growth in a chemostat. Zbl 0878.92032
Smith, H. L.
1997
Periodic tridiagonal competitive and cooperative systems of differential equations. Zbl 0746.34030
Smith, Hal L.
1991
Asymptotically stable equilibria for monotone semiflows. Zbl 1110.37061
Hirsch, M. W.; Smith, H. L.
2006
The Freter model: A simple model of biofilm formation. Zbl 1023.92010
Jones, Don; Kojouharov, Hristo V.; Le, Dung; Smith, Hal
2003
Global dynamics of microbial competition for two resources with internal storage. Zbl 1125.92058
Li, Bingtuan; Smith, Hal L.
2007
Dynamics of stoichiometric bacteria-algae interactions in the epilimnion. Zbl 1133.92031
Wang, Hao; Smith, Hal L.; Kuang, Yang; Elser, James J.
2007
Lyapunov exponents and persistence in discrete dynamical systems. Zbl 1175.34067
Salceanu, Paul L.; Smith, H. L.
2009
Competition in the gradostat: The role of the communication rate. Zbl 0716.92025
Smith, Hal; Tang, Betty
1989
Global stability for mixed monotone systems. Zbl 1162.39009
Smith, H. L.
2008
Competitive exclusion in a discrete-time, size-structured chemostat model. Zbl 1056.92059
Smith, H. L.; Zhao, X.-Q.
2001
An abstract threshold theorem for one parameter families of positive noncompact operators. Zbl 0476.47041
Smith, Hal L.
1981
Existence and uniqueness of global solutions for a size-structured model of an insect population with variable instar duration. Zbl 0810.92022
Smith, Hal L.
1994
Competitive and cooperative systems: mini-review. Zbl 1134.92358
Hirsch, Morris W.; Smith, Hal L.
2003
A resource-based model of microbial quiescence. Zbl 1098.92067
Malik, Tufail; Smith, Hal
2006
A discrete, size-structured model of microbial growth and competition in the chemostat. Zbl 0884.92029
Smith, H. L.
1996
Periodic coexistence of four species competing for three essential resources. Zbl 1018.92031
Li, Bingtuan; Smith, Hal L.
2003
Global stability for infinite-delay, dispersive Lotka-Volterra systems: Weakly interacting populations in nearly identical patches. Zbl 0731.92029
Kuang, Y.; Smith, H. L.; Martin, R. H.
1991
Competition for essential resources: a brief review. Zbl 1162.92334
Smith, Hal L.; Li, Bingtuan
2003
Persistence and global stability for a class of discrete time structured population models. Zbl 1306.37099
Smith, Hal L.; Thieme, Horst R.
2013
Persistence of bacteria and phages in a chemostat. Zbl 1303.92123
Smith, Hal L.; Thieme, Horst R.
2012
The pharmacodynamics of antibiotic treatment. Zbl 1111.92033
Mudassar, Imran; Smith, Hal
2006
Competition in a chemostat with wall attachment. Zbl 0992.92017
Stemmons, Eric D.; Smith, Hal L.
2000
Hopf bifurcation in a system of functional equations modeling the spread of an infectious disease. Zbl 0524.92019
Smith, Hal
1983
Stable periodic orbits for a predator-prey model with delay. Zbl 0997.92035
Cavani, Mario; Lizana, Marcos; Smith, Hal L.
2000
Convergence in Lotka-Volterra type diffusive delay systems without dominating instantaneous negative feedbacks. Zbl 0807.35149
Kuang, Yang; Smith, Hal L.
1993
Persistence and critical domain size for diffusing populations with two sexes and short reproductive season. Zbl 1369.92097
Jin, Wen; Smith, Hal L.; Thieme, Horst R.
2016
Models of virulent phage growth with application to phage therapy. Zbl 1151.92316
Smith, Hal L.
2008
Chemostats and epidemics: competition for nutrients/hosts. Zbl 1273.92039
Smith, Hal L.; Thieme, Horst R.
2013
Persistence in a discrete-time, stage-structured epidemic model. Zbl 1182.92063
Salceanu, Paul Leonard; Smith, Hal L.
2010
Does dormancy increase fitness of bacterial populations in time-varying environments? Zbl 1142.92045
Malik, Tufail; Smith, Hal L.
2008
Growth in the unstirred chemostat with different diffusion rates. Zbl 0920.35076
Le Dung; Smith, Hal L.; Waltman, P.
1999
Convergence in Lotka-Volterra-type delay systems without instantaneous feedbacks. Zbl 0795.34067
Kuang, Yang; Smith, Hal L.
1993
Equivalent dynamics for a structured population model and a related functional differential equation. Zbl 0835.34090
Smith, Hal L.
1995
On real-valued SDE and nonnegative-valued SDE population models with demographic variability. Zbl 1448.60120
Allen, E. J.; Allen, L. J. S.; Smith, H. L.
2020
Monotone dynamical systems: reflections on new advances & applications. Zbl 1357.34002
Smith, Hal L.
2017
Persistence in phage-bacteria communities with nested and one-to-one infection networks. Zbl 1360.92100
Korytowski, Dan A.; Smith, Hal L.
2017
Competition in the chemostat with time-dependent differential removal rates. Zbl 1372.92061
Fan, Guihong; Smith, Hal L.; Thieme, Horst R.
2017
Permanence and stability of a kill the winner model in marine ecology. Zbl 1368.92145
Korytowski, Daniel A.; Smith, Hal
2017
Persistence and critical domain size for diffusing populations with two sexes and short reproductive season. Zbl 1369.92097
Jin, Wen; Smith, Hal L.; Thieme, Horst R.
2016
Persistence versus extinction for a class of discrete-time structured population models. Zbl 1347.37126
Jin, Wen; Smith, Hal L.; Thieme, Horst R.
2016
Spread of phage infection of bacteria in a petri dish. Zbl 1336.92082
Jones, Don A.; Smith, Hal L.; Thieme, Horst R.
2016
A special class of Lotka-Volterra models of bacteria-virus infection networks. Zbl 1367.92120
Korytowski, Daniel A.; Smith, Hal L.
2016
A model of optimal dosing of antibiotic treatment in biofilm. Zbl 1298.92050
Imran, Mudassar; Smith, Hal L.
2014
Niche partitioning along an environmental gradient. Zbl 1345.92162
Klapper, Isaac; Dockery, Jack; Smith, Hal
2014
Persistence and global stability for a class of discrete time structured population models. Zbl 1306.37099
Smith, Hal L.; Thieme, Horst R.
2013
Chemostats and epidemics: competition for nutrients/hosts. Zbl 1273.92039
Smith, Hal L.; Thieme, Horst R.
2013
Spread of viral infection of immobilized bacteria. Zbl 1267.92050
Jones, Don A.; Smith, Hal L.; Thieme, Horst R.
2013
Persistence of bacteria and phages in a chemostat. Zbl 1303.92123
Smith, Hal L.; Thieme, Horst R.
2012
Bacteriophage-resistant and bacteriophage-sensitive bacteria in a chemostat. Zbl 1260.92115
Han, Zhun; Smith, Hal L.
2012
On spread of phage infection of bacteria in a Petri dish. Zbl 1243.92041
Jones, Don A.; Smith, Hal L.; Thieme, Horst R.; Röst, Gergely
2012
Global dynamics of the smallest chemical reaction system with Hopf bifurcation. Zbl 1306.92082
Smith, Hal L.
2012
Global dynamics of a discrete two-species Lottery-Ricker competition model. Zbl 1448.92205
Kang, Yun; Smith, Hal
2012
An introduction to delay differential equations with applications to the life sciences. Zbl 1227.34001
Smith, Hal
2011
Dynamical systems and population persistence. Zbl 1214.37002
Smith, Hal L.; Thieme, Horst R.
2011
Bacterial competition in serial transfer culture. Zbl 1208.92092
Smith, Hal L.
2011
Well-posedness and dissipativity for a model of bacteriophage and bacteria in a flow reactor. Zbl 1228.34121
Smith, Hal L.
2011
Bacteriophage and bacteria in a flow reactor. Zbl 1334.92258
Jones, Don A.; Smith, Hal L.
2011
Persistence in a discrete-time, stage-structured epidemic model. Zbl 1182.92063
Salceanu, Paul Leonard; Smith, Hal L.
2010
Lyapunov exponents and persistence in discrete dynamical systems. Zbl 1175.34067
Salceanu, Paul L.; Smith, H. L.
2009
Persistence in a discrete-time stage-structured fungal disease model. Zbl 1342.92278
Salceanu, Paul Leonard; Smith, Hal L.
2009
Lyapunov exponents and uniform weak normally repelling invariant sets. Zbl 1185.37054
Salceanu, Paul Leonard; Smith, Hal L.
2009
Bacteriophage infection dynamics: multiple host binding sites. Zbl 1183.92075
Smith, H. L.; Trevino, R. T.
2009
The theory of the chemostat. Dynamics of microbial competition. Reprint of the 1995 hardback ed. Zbl 1139.92029
Smith, Hal L.; Waltman, Paul
2008
Global stability for mixed monotone systems. Zbl 1162.39009
Smith, H. L.
2008
Models of virulent phage growth with application to phage therapy. Zbl 1151.92316
Smith, Hal L.
2008
Does dormancy increase fitness of bacterial populations in time-varying environments? Zbl 1142.92045
Malik, Tufail; Smith, Hal L.
2008
Prevalent behavior of strongly order preserving semiflows. Zbl 1178.37014
Enciso, Germán A.; Hirsch, Morris W.; Smith, Hal L.
2008
Global dynamics of microbial competition for two resources with internal storage. Zbl 1125.92058
Li, Bingtuan; Smith, Hal L.
2007
Dynamics of stoichiometric bacteria-algae interactions in the epilimnion. Zbl 1133.92031
Wang, Hao; Smith, Hal L.; Kuang, Yang; Elser, James J.
2007
The dynamics of bacterial infection, innate immune response, and antibiotic treatment. Zbl 1128.92017
Imran, Mudassar; Smith, H. L.
2007
The discrete dynamics of monotonically decomposable maps. Zbl 1118.65057
Smith, H. L.
2006
Nonmonotone systems decomposable into monotone systems with negative feedback. Zbl 1103.34021
Enciso, G. A.; Smith, H. L.; Sontag, E. D.
2006
Asymptotically stable equilibria for monotone semiflows. Zbl 1110.37061
Hirsch, M. W.; Smith, H. L.
2006
A resource-based model of microbial quiescence. Zbl 1098.92067
Malik, Tufail; Smith, Hal
2006
The pharmacodynamics of antibiotic treatment. Zbl 1111.92033
Mudassar, Imran; Smith, Hal
2006
Multiple limit cycles in the standard model of three species competition for three essential resources. Zbl 1110.92046
Baer, Steven M.; Li, Bingtuan; Smith, Hal L.
2006
Monotone dynamical systems. Zbl 1094.34003
Hirsch, M. W.; Smith, Hal
2005
Monotone maps: a review. Zbl 1080.37016
Hirsch, M. W.; Smith, Hal
2005
Biofilms and the plasmid maintenance question. Zbl 1064.92044
Imran, Mudassar; Jones, Don; Smith, Hal
2005
Traveling waves in a bio-reactor model. Zbl 1079.35011
Smith, Hal L.; Zhao, Xiao-Qiang
2004
Generic quasi-convergence for strongly order preserving semiflows: a new approach. Zbl 1074.34042
Hirsch, Morris W.; Smith, Hal L.
2004
Virus dynamics: a global analysis. Zbl 1035.34045
De Leenheer, Patrick; Smith, Hal L.
2003
Feedback control for chemostat models. Zbl 1015.92046
De Leenheer, Patrick; Smith, Hal
2003
Competition in the chemostat: some remarks. Zbl 1132.92341
De Leenheer, Patrick; Li, Bingtuan; Smith, Hal L.
2003
The Freter model: A simple model of biofilm formation. Zbl 1023.92010
Jones, Don; Kojouharov, Hristo V.; Le, Dung; Smith, Hal
2003
Competitive and cooperative systems: mini-review. Zbl 1134.92358
Hirsch, Morris W.; Smith, Hal L.
2003
Periodic coexistence of four species competing for three essential resources. Zbl 1018.92031
Li, Bingtuan; Smith, Hal L.
2003
Competition for essential resources: a brief review. Zbl 1162.92334
Smith, Hal L.; Li, Bingtuan
2003
Bacterial wall attachment in a flow reactor. Zbl 1017.92034
Jones, Don; Kojouharov, Hristo V.; Le, Dung; Smith, Hal
2002
Strong positivity of solutions to parabolic and elliptic equations on nonsmooth domains. Zbl 1072.35503
Le, Dung; Smith, Hal
2002
Bacterial wall attachment in flow reactor: Mixed culture. Zbl 1027.92028
Jones, Don; Kojouharov, Hristo V.; Le, Dung; Smith, Hal
2002
Robust persistence for semidynamical systems. Zbl 1042.37504
Smith, Hal L.; Zhao, Xiao-Qiang
2001
Global dynamics of an SEIR epidemic model with vertical transmission. Zbl 0991.92029
Li, Michael Y.; Smith, Hal L.; Wang, Liancheng
2001
Chain transitivity, attractivity, and strong repellors for semidynamical systems. Zbl 1129.37306
Hirsch, Morris W.; Smith, Hal L.; Zhao, Xiao-Qiang
2001
Stable coexistence and bi-stability for competitive systems on ordered Banach spaces. Zbl 1064.47075
Smith, H. L.; Thieme, H. R.
2001
How many species can two essential resources support? Zbl 0992.92040
Li, Bingtuan; Smith, Hal
2001
Competitive exclusion in a discrete-time, size-structured chemostat model. Zbl 1056.92059
Smith, H. L.; Zhao, X.-Q.
2001
Global asymptotic stability of traveling waves in delayed reaction-diffusion equations. Zbl 0941.35125
Smith, Hal L.; Zhao, Xiao-Qiang
2000
Competition in a chemostat with wall attachment. Zbl 0992.92017
Stemmons, Eric D.; Smith, Hal L.
2000
Stable periodic orbits for a predator-prey model with delay. Zbl 0997.92035
Cavani, Mario; Lizana, Marcos; Smith, Hal L.
2000
Microbial competition for nutrient and wall sites in plug flow. Zbl 1013.92047
Jones, Don A.; Smith, Hal
2000
Microbial growth in a plug flow reactor with wall adherence and cell motility. Zbl 0999.92039
Smith, Hal; Zhao, Xiao-Qiang
2000
Competition in the periodic gradostat. Zbl 1004.92036
Smith, H. L.; Waltman, Paul
2000
A semilinear hyperbolic system. Zbl 0971.35048
Smith, Hal
2000
Effects of random motility on microbial growth and competition in a flow reactor. Zbl 1051.92039
Ballyk, Mary; Dung, Le; Jones, Don A.; Smith, Hal L.
1999
Perturbation of a globally stable steady state. Zbl 0924.58087
Smith, H. L.; Waltman, P.
1999
Dynamics of a periodically pulsed bio-reactor model. Zbl 0930.35085
Smith, Hal L.; Zhao, Xiao-Qiang
1999
A model of microbial growth in a plug flow reactor with wall attachment. Zbl 0980.92034
Ballyk, Mary; Smith, Hal
1999
Steady states of models of microbial growth and competition with chemotaxis. Zbl 0933.35088
Le Dung; Smith, Hal L.
1999
Dynamics of competition. Zbl 1002.92564
Smith, H. L.
1999
Growth in the unstirred chemostat with different diffusion rates. Zbl 0920.35076
Le Dung; Smith, Hal L.; Waltman, P.
1999
Competition between plasmid-bearing and plasmid-free microorganisms in a chemostat with distinct removal rates. Zbl 0977.92030
Li, Bingtuan; Kuang, Yang; Smith, Hal L.
1999
Planar competitive and cooperative difference equations. Zbl 0907.39004
Smith, H. L.
1998
A flow reactor with wall growth. Zbl 0929.92034
Ballyk, Mary M.; Smith, Hal L.
1998
Global existence of periodic solutions in a class of delayed Gause-type predator-prey systems. Zbl 0872.34047
Zhao, Tao; Kuang, Yang; Smith, H. L.
1997
The periodically forced Droop model for phytoplankton growth in a chemostat. Zbl 0878.92032
Smith, H. L.
1997
Complicated dynamics for low-dimensional strongly monotone maps. Zbl 0893.54034
Smith, H. L.
1997
Competitive exclusion and coexistence for competitive systems on ordered Banach spaces. Zbl 0860.47033
Hsu, S. B.; Smith, H. L.; Waltman, Paul
1996
A parabolic system modeling microbial competition in an unmixed bio-reactor. Zbl 0865.35017
Le Dung; Smith, Hal L.
1996
A discrete, size-structured model of microbial growth and competition in the chemostat. Zbl 0884.92029
Smith, H. L.
1996
Competition in an unstirred multi-dimensional chemostat. Zbl 0934.35074
Smith, Hal L.; Waltman, Paul
1996
An application of monotone systems theory to a model of microbial competition. Zbl 0858.92030
Smith, Hal L.
1996
Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems. Zbl 0821.34003
Smith, Hal L.
1995
The theory of the chemostat. Dynamics of microbial competition. Zbl 0860.92031
Smith, Hal L.; Waltman, Paul
1995
Asymptotically autonomous semiflows: Chain recurrence and Lyapunov functions. Zbl 0829.34037
Mischaikow, Konstantin; Smith, Hal; Thieme, Horst R.
1995
Equivalent dynamics for a structured population model and a related functional differential equation. Zbl 0835.34090
Smith, Hal L.
1995
On the existence and stability of bounded almost periodic and periodic solutions of a singularly perturbed nonautonomous system. Zbl 0835.34071
Smith, Hal L.
1995
Tridiagonal competitive-cooperative Kolmogorov systems. Zbl 0870.92018
Freedman, H. I.; Smith, H. L.
1995
Dynamics of competition in the unstirred chemostat. Zbl 0831.92028
Hsu, S. B.; Smith, H. L.; Waltman, Paul
1994
Stable periodic orbits for a class of three dimensional competitive systems. Zbl 0802.34064
Zhu, Hsiu-Rong; Smith, Hal L.
1994
Competition for a single limiting resource in continuous culture: The variable-yield model. Zbl 0829.92020
Smith, Hal L.; Waltman, Paul
1994
A structured population model and a related functional differential equation: Global attractors and uniform persistence. Zbl 0794.34061
Smith, Hal L.
1994
Existence and uniqueness of global solutions for a size-structured model of an insect population with variable instar duration. Zbl 0810.92022
Smith, Hal L.
1994
...and 62 more Documents
all top 5

#### Cited by 3,562 Authors

 76 Smith, Hal Leslie 75 Zhao, Xiao-Qiang 59 Chen, Lansun 58 Wu, Jianhong 43 Zou, Xingfu 42 Jiang, Jifa 42 Wang, Feng-Bin 39 Li, Wan-Tong 38 Kulenović, Mustafa R. S. 38 Teng, Zhi-dong 36 Ruan, Shigui 31 Ma, Wanbiao 30 Hsu, Szebi 29 Wang, Jinliang 29 Wang, Wendi 28 Thieme, Horst R. 27 Lou, Yuan 27 Takeuchi, Yasuhiro 25 Obaya, Rafael 25 Yuan, Rong 24 Chen, Yuming 24 Nie, Hua 24 Sontag, Eduardo D. 23 Kuniya, Toshikazu 23 Liu, Shengqiang 23 Wu, Jianhua 22 Kuang, Yang 22 Li, Xuezhi 22 Liu, Xianning 22 Song, Xinyu 22 Xu, Rui 21 Qiu, Zhipeng 21 Wei, Junjie 21 Wu, Shiliang 20 Jang, Sophia R.-J. 20 Jin, Zhen 20 Lin, Guo 20 Shi, Junping 20 Yuan, Sanling 19 Lam, King-Yeung 19 Rapaport, Alain 19 Yi, Taishan 18 De Leenheer, Patrick 18 Wang, Yi 17 Cui, Jingan 17 Faria, Teresa 17 Gouzé, Jean-Luc 17 Weng, Peixuan 16 Gourley, Stephen A. 16 Gumel, Abba B. 16 Jiang, Daqing 16 Lou, Yijun 16 Sanz, Ana M. 16 Wang, Lin 15 Ackleh, Azmy S. 15 Cai, Liming 15 Gyllenberg, Mats 15 Niu, Lei 15 Wolkowicz, Gail S. K. 14 Gedeon, Tomáš 14 Guo, Shangjiang 14 Liu, Zhijun 14 Lutscher, Frithjof 14 Magal, Pierre 14 Martcheva, Maia 14 Ruiz-Herrera, Alfonso 14 Trofimchuk, Sergei I. 14 Yang, Yu 14 Zhang, Long 13 Angeli, David 13 Hsu, Cheng-Hsiung 13 Meng, Xinzhu 13 Wang, Wei 13 Zhang, Tonghua 13 Zhou, Yicang 12 Caraballo Garrido, Tomás 12 Gao, Daozhou 12 Huang, Lihong 12 Huo, Hai-Feng 12 Li, Michael Yi 12 Liu, Rongsong 12 Mierczyński, Janusz 12 Röst, Gergely 12 Sari, Tewfik 12 Waltman, Paul Elvis 12 Wang, Hao 12 Xiao, Dongmei 11 Cushing, Jim M. 11 Eberl, Hermann J. 11 Hadeler, Karl-Peter 11 Harmand, Jérôme 11 Liu, Junli 11 Pilyugin, Sergei S. 11 Wang, Xia 11 Wu, Fuke 11 Xiao, Yanni 10 Allen, Linda J. S. 10 Buonomo, Bruno 10 Cosner, Chris 10 Elaiw, Ahmed M. ...and 3,462 more Authors
all top 5

#### Cited in 297 Serials

 211 Journal of Differential Equations 210 Journal of Mathematical Analysis and Applications 169 Journal of Mathematical Biology 167 Applied Mathematics and Computation 157 Mathematical Biosciences 155 Nonlinear Analysis. Real World Applications 147 Discrete and Continuous Dynamical Systems. Series B 103 Bulletin of Mathematical Biology 86 Journal of Dynamics and Differential Equations 78 Journal of Biological Dynamics 62 Journal of Difference Equations and Applications 60 International Journal of Biomathematics 60 Journal of Theoretical Biology 59 Advances in Difference Equations 53 Chaos, Solitons and Fractals 53 Mathematical Biosciences and Engineering 51 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 49 Computers & Mathematics with Applications 48 Discrete Dynamics in Nature and Society 45 Automatica 42 Abstract and Applied Analysis 41 Mathematical Methods in the Applied Sciences 38 Applied Mathematical Modelling 38 Discrete and Continuous Dynamical Systems 37 SIAM Journal on Applied Mathematics 36 Proceedings of the American Mathematical Society 35 Journal of Computational and Applied Mathematics 35 Applied Mathematics Letters 33 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 33 Communications in Nonlinear Science and Numerical Simulation 33 Nonlinear Analysis. Theory, Methods & Applications 30 Theoretical Population Biology 27 Applicable Analysis 27 Communications on Pure and Applied Analysis 27 Journal of Applied Mathematics and Computing 26 Mathematical and Computer Modelling 24 Nonlinear Dynamics 24 Journal of Biological Systems 23 Systems & Control Letters 23 Physica D 21 Journal of the Franklin Institute 20 Rocky Mountain Journal of Mathematics 20 Journal of Applied Analysis and Computation 19 Journal of Mathematical Chemistry 19 Differential Equations and Dynamical Systems 19 SIAM Journal on Applied Dynamical Systems 15 Transactions of the American Mathematical Society 15 Complexity 15 Discrete and Continuous Dynamical Systems. Series S 13 Nonlinearity 13 Mathematics and Computers in Simulation 12 International Journal of Control 12 Acta Applicandae Mathematicae 12 Journal of Nonlinear Science 12 Mathematical Problems in Engineering 11 Acta Mathematicae Applicatae Sinica. English Series 11 European Journal of Applied Mathematics 11 Journal of Applied Mathematics 10 ZAMP. Zeitschrift für angewandte Mathematik und Physik 10 Ricerche di Matematica 10 European Journal of Control 10 Mathematical Modelling of Natural Phenomena 9 SIAM Journal on Mathematical Analysis 9 Computational and Applied Mathematics 9 Acta Mathematica Sinica. English Series 9 Nonlinear Analysis. Hybrid Systems 8 SIAM Journal on Control and Optimization 8 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 8 Chaos 8 Science China. Mathematics 7 International Journal of Robust and Nonlinear Control 7 Computational & Mathematical Methods in Medicine 7 International Journal of Applied and Computational Mathematics 6 Journal of Functional Analysis 6 Applied Mathematics and Mechanics. (English Edition) 6 Japan Journal of Industrial and Applied Mathematics 6 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 6 Wuhan University Journal of Natural Sciences (WUJNS) 6 Dynamical Systems 6 Mediterranean Journal of Mathematics 6 Journal of Nonlinear Science and Applications 6 International Journal of Differential Equations 5 Quarterly of Applied Mathematics 5 Ergodic Theory and Dynamical Systems 5 Applied Numerical Mathematics 5 MCSS. Mathematics of Control, Signals, and Systems 5 International Journal of Computer Mathematics 5 Linear Algebra and its Applications 5 Stochastic Processes and their Applications 5 Applied Mathematics. Series B (English Edition) 5 Calculus of Variations and Partial Differential Equations 5 Electronic Journal of Differential Equations (EJDE) 5 Journal of Evolution Equations 5 Nonautonomous Dynamical Systems 4 Archive for Rational Mechanics and Analysis 4 International Journal of Systems Science 4 Journal of Mathematical Physics 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Annales Polonici Mathematici 4 Results in Mathematics ...and 197 more Serials
all top 5

#### Cited in 50 Fields

 2,517 Biology and other natural sciences (92-XX) 1,719 Ordinary differential equations (34-XX) 861 Partial differential equations (35-XX) 720 Dynamical systems and ergodic theory (37-XX) 269 Systems theory; control (93-XX) 176 Numerical analysis (65-XX) 163 Difference and functional equations (39-XX) 148 Operator theory (47-XX) 131 Probability theory and stochastic processes (60-XX) 95 Integral equations (45-XX) 67 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 58 Calculus of variations and optimal control; optimization (49-XX) 29 Computer science (68-XX) 22 Combinatorics (05-XX) 20 Operations research, mathematical programming (90-XX) 19 Global analysis, analysis on manifolds (58-XX) 17 Linear and multilinear algebra; matrix theory (15-XX) 15 General topology (54-XX) 15 Statistics (62-XX) 11 Real functions (26-XX) 11 Functional analysis (46-XX) 10 Mechanics of particles and systems (70-XX) 10 Fluid mechanics (76-XX) 10 Classical thermodynamics, heat transfer (80-XX) 8 Statistical mechanics, structure of matter (82-XX) 8 Information and communication theory, circuits (94-XX) 6 General and overarching topics; collections (00-XX) 6 Mechanics of deformable solids (74-XX) 5 Measure and integration (28-XX) 5 Geophysics (86-XX) 4 Approximations and expansions (41-XX) 4 Mathematics education (97-XX) 3 Functions of a complex variable (30-XX) 3 Abstract harmonic analysis (43-XX) 3 Optics, electromagnetic theory (78-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Topological groups, Lie groups (22-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Algebraic topology (55-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Group theory and generalizations (20-XX) 1 Special functions (33-XX) 1 Integral transforms, operational calculus (44-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Manifolds and cell complexes (57-XX) 1 Quantum theory (81-XX)