Edit Profile (opens in new tab) Smith, Hal Leslie Compute Distance To: Compute Author ID: smith.hal-leslie Published as: Smith, Hal L.; Smith, H. L.; Smith, Hal; Smith, Hal Leslie more...less Homepage: https://math.la.asu.edu/~halsmith/ External Links: MGP Documents Indexed: 177 Publications since 1976, including 6 Books 2 Contributions as Editor Co-Authors: 64 Co-Authors with 118 Joint Publications 2,110 Co-Co-Authors 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 De Leenheer, Patrick 4 Kojouharov, Hristo V. 4 Martin, Robert H. jun. 4 Salceanu, Paul Leonard 4 Schmitt, Klaus 3 Ballyk, Mary M. 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 M. 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 Capasso, Vincenzo 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 Schuster, Martin R. 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 4 Mathematical Biosciences and Engineering 3 Bulletin of Mathematical Biology 3 Transactions of the American Mathematical Society 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 2 Cambridge Studies in Mathematical Biology 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 127 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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 162 Publications have been cited 6,017 times in 3,974 Documents Cited by ▼ Year ▼ Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems. Zbl 0821.34003Smith, Hal L. 785 1995 The theory of the chemostat. Dynamics of microbial competition. Zbl 0860.92031Smith, Hal L.; Waltman, Paul 466 1995 Abstract functional differential equations and reaction-diffusion systems. Zbl 0722.35046Martin, R. H. jun.; Smith, H. L. 313 1990 An introduction to delay differential equations with applications to the life sciences. Zbl 1227.34001Smith, Hal 243 2011 Dynamical systems and population persistence. Zbl 1214.37002Smith, Hal L.; Thieme, Horst R. 203 2011 Virus dynamics: a global analysis. Zbl 1035.34045De Leenheer, Patrick; Smith, Hal L. 199 2003 Robust persistence for semidynamical systems. Zbl 1042.37504Smith, Hal L.; Zhao, Xiao-Qiang 156 2001 Global asymptotic stability of traveling waves in delayed reaction-diffusion equations. Zbl 0941.35125Smith, Hal L.; Zhao, Xiao-Qiang 121 2000 Planar competitive and cooperative difference equations. Zbl 0907.39004Smith, H. L. 115 1998 Global dynamics of an SEIR epidemic model with vertical transmission. Zbl 0991.92029Li, Michael Y.; Smith, Hal L.; Wang, Liancheng 114 2001 Competitive exclusion and coexistence for competitive systems on ordered Banach spaces. Zbl 0860.47033Hsu, S. B.; Smith, H. L.; Waltman, Paul 108 1996 Cooperative systems of differential equations with concave nonlinearities. Zbl 0612.34035Smith, H. L. 107 1986 Asymptotically autonomous semiflows: Chain recurrence and Lyapunov functions. Zbl 0829.34037Mischaikow, Konstantin; Smith, Hal; Thieme, Horst R. 101 1995 Global stability for infinite delay Lotka–Volterra type systems. Zbl 0786.34077Kuang, Y.; Smith, H. L. 100 1993 Chain transitivity, attractivity, and strong repellors for semidynamical systems. Zbl 1129.37306Hirsch, Morris W.; Smith, Hal L.; Zhao, Xiao-Qiang 99 2001 Systems of ordinary differential equations which generate an order preserving flow. A survey of results. Zbl 0674.34012Smith, Hal L. 96 1988 Monotone dynamical systems. Zbl 1094.34003Hirsch, M. W.; Smith, Hal 93 2005 The Poincaré-Bendixson theorem for monotone cyclic feedback systems. Zbl 0712.34060Mallet-Paret, John; Smith, Hal L. 91 1990 Monotone semiflows generated by functional differential equations. Zbl 0612.34067Smith, Hal 91 1987 Infinite subharmonic bifurcation in an SEIR epidemic model. Zbl 0523.92020Schwartz, Ira B.; Smith, H. L. 85 1983 Reaction-diffusion systems with time delays: Monotonicity, invariance, comparison and convergence. Zbl 0709.35059Martin, R. H. jun.; Smith, H. L. 79 1991 Effects of random motility on microbial growth and competition in a flow reactor. Zbl 1051.92039Ballyk, Mary; Dung, Le; Jones, Don A.; Smith, Hal L. 74 1999 The theory of the chemostat. Dynamics of microbial competition. Reprint of the 1995 hardback ed. Zbl 1139.92029Smith, Hal L.; Waltman, Paul 70 2008 Competitive coexistence in an oscillating chemostat. Zbl 0467.92018Smith, Hal L. 68 1981 Periodic competitive differential equations and the discrete dynamics of competitive maps. Zbl 0596.34013Smith, Hal L. 64 1986 Strongly order preserving semiflows generated by functional differential equations. Zbl 0735.34065Smith, Hal L.; Thieme, Horst R. 64 1991 Global existence of periodic solutions in a class of delayed Gause-type predator-prey systems. Zbl 0872.34047Zhao, Tao; Kuang, Yang; Smith, H. L. 63 1997 Perturbation of a globally stable steady state. Zbl 0924.58087Smith, H. L.; Waltman, P. 49 1999 Feedback control for chemostat models. Zbl 1015.92046De Leenheer, Patrick; Smith, Hal 47 2003 Monotone maps: a review. Zbl 1080.37016Hirsch, M. W.; Smith, Hal 46 2005 Periodic solutions of periodic competitive and cooperative systems. Zbl 0609.34048Smith, Hal L. 44 1986 A parabolic system modeling microbial competition in an unmixed bio-reactor. Zbl 0865.35017Le Dung; Smith, Hal L. 43 1996 Slowly oscillating periodic solutions of autonomous state-dependent delay equations. Zbl 0774.34054Kuang, Y.; Smith, H. L. 43 1992 Convergence for strongly order-preserving semiflows. Zbl 0739.34040Smith, Hal L.; Thieme, Horst R. 41 1991 On the asymptotic behavior of a class of deterministic models of cooperating species. Zbl 0607.92023Smith, Hal L. 40 1986 Subharmonic bifurcation in an S-I-R epidemic model. Zbl 0578.92023Smith, H. L. 39 1983 Periodic solutions of differential delay equations with threshold-type delays. Zbl 0762.34044Smith, H. L.; Kuang, Y. 38 1992 Competing subcommunities of mutualists and a generalized Kamke theorem. Zbl 0609.92033Smith, Hal L. 37 1986 Reduction of structured population models to threshold-type delay equations and functional differential equations: A case study. Zbl 0797.92024Smith, Hal L. 36 1993 Dynamics of competition in the unstirred chemostat. Zbl 0831.92028Hsu, S. B.; Smith, H. L.; Waltman, Paul 35 1994 Quasi convergence and stability for strongly order-preserving semiflows. Zbl 0704.34054Smith, Hal L.; Thieme, Horst R. 32 1990 Invariant curves for mappings. Zbl 0606.47056Smith, Hal L. 32 1986 Multiple stable subharmonics for a periodic epidemic model. Zbl 0529.92018Smith, H. L. 32 1983 The interaction of steady state and Hopf bifurcations in a two-predator- one-prey competition model. Zbl 0489.92019Smith, Hal L. 30 1982 On periodic solutions of a delay integral equation modelling epidemics. Zbl 0354.92035Smith, H. L. 30 1977 Dynamics of a periodically pulsed bio-reactor model. Zbl 0930.35085Smith, Hal L.; Zhao, Xiao-Qiang 30 1999 Stable periodic orbits for a class of three dimensional competitive systems. Zbl 0802.34064Zhu, Hsiu-Rong; Smith, Hal L. 30 1994 Competition for a single limiting resource in continuous culture: The variable-yield model. Zbl 0829.92020Smith, Hal L.; Waltman, Paul 30 1994 Monotone semiflows in scalar non-quasi-monotone functional differential equations. Zbl 0719.34123Smith, Hal L.; Thieme, Horst R. 28 1990 Periodic orbits of competitive and cooperative systems. Zbl 0615.34027Smith, Hal L. 28 1986 Oscillations and multiple steady states in a cyclic gene model with repression. Zbl 0619.92004Smith, Hal 28 1987 A model of microbial growth in a plug flow reactor with wall attachment. Zbl 0980.92034Ballyk, Mary; Smith, Hal 28 1999 On eigenvalue problems for nondifferentiable mappings. Zbl 0389.34019Schmitt, K.; Smith, H. L. 28 1979 Fixed point techniques in a cone with applications. Zbl 0435.47060Gatica, J. A.; Smith, Hal L. 28 1977 Stable coexistence and bi-stability for competitive systems on ordered Banach spaces. Zbl 1064.47075Smith, H. L.; Thieme, H. R. 24 2001 How many species can two essential resources support? Zbl 0992.92040Li, Bingtuan; Smith, Hal 24 2001 Global stability in diffusive delay Lotka-Volterra systems. Zbl 0752.34041Kuang, Y.; Smith, H. L. 22 1991 Competition in an \(n\)-vessel gradostat. Zbl 0749.92024Smith, H. L.; Tang, Betty; Waltman, Paul 22 1991 The discrete dynamics of monotonically decomposable maps. Zbl 1118.65057Smith, H. L. 21 2006 Positive solutions and conjugate points for systems of differential equations. Zbl 0379.34015Schmitt, K.; Smith, H. L. 21 1978 Stable periodic solutions for the hypercycle system. Zbl 0729.34032Hofbauer, J.; Mallet-Paret, J.; Smith, H. L. 20 1991 Dynamics of stoichiometric bacteria-algae interactions in the epilimnion. Zbl 1133.92031Wang, Hao; Smith, Hal L.; Kuang, Yang; Elser, James J. 20 2007 Steady states of models of microbial growth and competition with chemotaxis. Zbl 0933.35088Le Dung; Smith, Hal L. 20 1999 A structured population model and a related functional differential equation: Global attractors and uniform persistence. Zbl 0794.34061Smith, Hal L. 20 1994 Nonmonotone systems decomposable into monotone systems with negative feedback. Zbl 1103.34021Enciso, G. A.; Smith, H. L.; Sontag, E. D. 19 2006 Dynamics of competition. Zbl 1002.92564Smith, H. L. 18 1999 Competition in the chemostat: some remarks. Zbl 1132.92341De Leenheer, Patrick; Li, Bingtuan; Smith, Hal L. 17 2003 Traveling waves in a bio-reactor model. Zbl 1079.35011Smith, Hal L.; Zhao, Xiao-Qiang 17 2004 The periodically forced Droop model for phytoplankton growth in a chemostat. Zbl 0878.92032Smith, H. L. 16 1997 The Freter model: A simple model of biofilm formation. Zbl 1023.92010Jones, Don; Kojouharov, Hristo V.; Le, Dung; Smith, Hal 16 2003 Periodic tridiagonal competitive and cooperative systems of differential equations. Zbl 0746.34030Smith, Hal L. 16 1991 Asymptotically stable equilibria for monotone semiflows. Zbl 1110.37061Hirsch, M. W.; Smith, H. L. 16 2006 Persistence and global stability for a class of discrete time structured population models. Zbl 1306.37099Smith, Hal L.; Thieme, Horst R. 15 2013 Competitive and cooperative systems: mini-review. Zbl 1134.92358Hirsch, Morris W.; Smith, Hal L. 15 2003 Global dynamics of microbial competition for two resources with internal storage. Zbl 1125.92058Li, Bingtuan; Smith, Hal L. 15 2007 Lyapunov exponents and persistence in discrete dynamical systems. Zbl 1175.34067Salceanu, Paul L.; Smith, H. L. 15 2009 Competition in the gradostat: The role of the communication rate. Zbl 0716.92025Smith, Hal; Tang, Betty 14 1989 Global stability for mixed monotone systems. Zbl 1162.39009Smith, H. L. 13 2008 Competitive exclusion in a discrete-time, size-structured chemostat model. Zbl 1056.92059Smith, H. L.; Zhao, X.-Q. 13 2001 Persistence and critical domain size for diffusing populations with two sexes and short reproductive season. Zbl 1369.92097Jin, Wen; Smith, Hal L.; Thieme, Horst R. 12 2016 Competition for essential resources: a brief review. Zbl 1162.92334Smith, Hal L.; Li, Bingtuan 12 2003 An abstract threshold theorem for one parameter families of positive noncompact operators. Zbl 0476.47041Smith, Hal L. 12 1981 A resource-based model of microbial quiescence. Zbl 1098.92067Malik, Tufail; Smith, Hal 12 2006 Existence and uniqueness of global solutions for a size-structured model of an insect population with variable instar duration. Zbl 0810.92022Smith, Hal L. 12 1994 Global stability for infinite-delay, dispersive Lotka-Volterra systems: Weakly interacting populations in nearly identical patches. Zbl 0731.92029Kuang, Y.; Smith, H. L.; Martin, R. H. 11 1991 Microbial competition for nutrient and wall sites in plug flow. Zbl 1013.92047Jones, Don A.; Smith, Hal 11 2000 Competition in a chemostat with wall attachment. Zbl 0992.92017Stemmons, Eric D.; Smith, Hal L. 11 2000 A discrete, size-structured model of microbial growth and competition in the chemostat. Zbl 0884.92029Smith, H. L. 11 1996 Periodic coexistence of four species competing for three essential resources. Zbl 1018.92031Li, Bingtuan; Smith, Hal L. 11 2003 Models of virulent phage growth with application to phage therapy. Zbl 1151.92316Smith, Hal L. 11 2008 Persistence of bacteria and phages in a chemostat. Zbl 1303.92123Smith, Hal L.; Thieme, Horst R. 11 2012 The pharmacodynamics of antibiotic treatment. Zbl 1111.92033Mudassar, Imran; Smith, Hal 10 2006 Does dormancy increase fitness of bacterial populations in time-varying environments? Zbl 1142.92045Malik, Tufail; Smith, Hal L. 10 2008 Convergence in Lotka-Volterra type diffusive delay systems without dominating instantaneous negative feedbacks. Zbl 0807.35149Kuang, Yang; Smith, Hal L. 10 1993 Persistence in a discrete-time, stage-structured epidemic model. Zbl 1182.92063Salceanu, Paul Leonard; Smith, Hal L. 10 2010 Hopf bifurcation in a system of functional equations modeling the spread of an infectious disease. Zbl 0524.92019Smith, Hal 9 1983 Stable periodic orbits for a predator-prey model with delay. Zbl 0997.92035Cavani, Mario; Lizana, Marcos; Smith, Hal L. 9 2000 Chemostats and epidemics: competition for nutrients/hosts. Zbl 1273.92039Smith, Hal L.; Thieme, Horst R. 9 2013 Persistence versus extinction for a class of discrete-time structured population models. Zbl 1347.37126Jin, Wen; Smith, Hal L.; Thieme, Horst R. 8 2016 Prevalent behavior of strongly order preserving semiflows. Zbl 1178.37014Enciso, Germán A.; Hirsch, Morris W.; Smith, Hal L. 8 2008 On real-valued SDE and nonnegative-valued SDE population models with demographic variability. Zbl 1448.60120Allen, E. J.; Allen, L. J. S.; Smith, H. L. 2 2020 Monotone dynamical systems: reflections on new advances & applications. Zbl 1357.34002Smith, Hal L. 8 2017 Persistence in phage-bacteria communities with nested and one-to-one infection networks. Zbl 1360.92100Korytowski, Dan A.; Smith, Hal L. 5 2017 Competition in the chemostat with time-dependent differential removal rates. Zbl 1372.92061Fan, Guihong; Smith, Hal L.; Thieme, Horst R. 1 2017 Permanence and stability of a kill the winner model in marine ecology. Zbl 1368.92145Korytowski, Daniel A.; Smith, Hal 1 2017 Persistence and critical domain size for diffusing populations with two sexes and short reproductive season. Zbl 1369.92097Jin, Wen; Smith, Hal L.; Thieme, Horst R. 12 2016 Persistence versus extinction for a class of discrete-time structured population models. Zbl 1347.37126Jin, Wen; Smith, Hal L.; Thieme, Horst R. 8 2016 Spread of phage infection of bacteria in a petri dish. Zbl 1336.92082Jones, Don A.; Smith, Hal L.; Thieme, Horst R. 2 2016 A special class of Lotka-Volterra models of bacteria-virus infection networks. Zbl 1367.92120Korytowski, Daniel A.; Smith, Hal L. 1 2016 A model of optimal dosing of antibiotic treatment in biofilm. Zbl 1298.92050Imran, Mudassar; Smith, Hal L. 4 2014 Niche partitioning along an environmental gradient. Zbl 1345.92162Klapper, Isaac; Dockery, Jack; Smith, Hal 2 2014 Persistence and global stability for a class of discrete time structured population models. Zbl 1306.37099Smith, Hal L.; Thieme, Horst R. 15 2013 Chemostats and epidemics: competition for nutrients/hosts. Zbl 1273.92039Smith, Hal L.; Thieme, Horst R. 9 2013 Spread of viral infection of immobilized bacteria. Zbl 1267.92050Jones, Don A.; Smith, Hal L.; Thieme, Horst R. 3 2013 Persistence of bacteria and phages in a chemostat. Zbl 1303.92123Smith, Hal L.; Thieme, Horst R. 11 2012 Bacteriophage-resistant and bacteriophage-sensitive bacteria in a chemostat. Zbl 1260.92115Han, Zhun; Smith, Hal L. 7 2012 On spread of phage infection of bacteria in a Petri dish. Zbl 1243.92041Jones, Don A.; Smith, Hal L.; Thieme, Horst R.; Röst, Gergely 4 2012 Global dynamics of the smallest chemical reaction system with Hopf bifurcation. Zbl 1306.92082Smith, Hal L. 3 2012 Global dynamics of a discrete two-species Lottery-Ricker competition model. Zbl 1448.92205Kang, Yun; Smith, Hal 1 2012 An introduction to delay differential equations with applications to the life sciences. Zbl 1227.34001Smith, Hal 243 2011 Dynamical systems and population persistence. Zbl 1214.37002Smith, Hal L.; Thieme, Horst R. 203 2011 Bacterial competition in serial transfer culture. Zbl 1208.92092Smith, Hal L. 3 2011 Well-posedness and dissipativity for a model of bacteriophage and bacteria in a flow reactor. Zbl 1228.34121Smith, Hal L. 3 2011 Bacteriophage and bacteria in a flow reactor. Zbl 1334.92258Jones, Don A.; Smith, Hal L. 2 2011 Persistence in a discrete-time, stage-structured epidemic model. Zbl 1182.92063Salceanu, Paul Leonard; Smith, Hal L. 10 2010 Lyapunov exponents and persistence in discrete dynamical systems. Zbl 1175.34067Salceanu, Paul L.; Smith, H. L. 15 2009 Persistence in a discrete-time stage-structured fungal disease model. Zbl 1342.92278Salceanu, Paul Leonard; Smith, Hal L. 5 2009 Lyapunov exponents and uniform weak normally repelling invariant sets. Zbl 1185.37054Salceanu, Paul Leonard; Smith, Hal L. 3 2009 Bacteriophage infection dynamics: multiple host binding sites. Zbl 1183.92075Smith, H. L.; Trevino, R. T. 3 2009 The theory of the chemostat. Dynamics of microbial competition. Reprint of the 1995 hardback ed. Zbl 1139.92029Smith, Hal L.; Waltman, Paul 70 2008 Global stability for mixed monotone systems. Zbl 1162.39009Smith, H. L. 13 2008 Models of virulent phage growth with application to phage therapy. Zbl 1151.92316Smith, Hal L. 11 2008 Does dormancy increase fitness of bacterial populations in time-varying environments? Zbl 1142.92045Malik, Tufail; Smith, Hal L. 10 2008 Prevalent behavior of strongly order preserving semiflows. Zbl 1178.37014Enciso, Germán A.; Hirsch, Morris W.; Smith, Hal L. 8 2008 Dynamics of stoichiometric bacteria-algae interactions in the epilimnion. Zbl 1133.92031Wang, Hao; Smith, Hal L.; Kuang, Yang; Elser, James J. 20 2007 Global dynamics of microbial competition for two resources with internal storage. Zbl 1125.92058Li, Bingtuan; Smith, Hal L. 15 2007 The dynamics of bacterial infection, innate immune response, and antibiotic treatment. Zbl 1128.92017Imran, Mudassar; Smith, H. L. 4 2007 The discrete dynamics of monotonically decomposable maps. Zbl 1118.65057Smith, H. L. 21 2006 Nonmonotone systems decomposable into monotone systems with negative feedback. Zbl 1103.34021Enciso, G. A.; Smith, H. L.; Sontag, E. D. 19 2006 Asymptotically stable equilibria for monotone semiflows. Zbl 1110.37061Hirsch, M. W.; Smith, H. L. 16 2006 A resource-based model of microbial quiescence. Zbl 1098.92067Malik, Tufail; Smith, Hal 12 2006 The pharmacodynamics of antibiotic treatment. Zbl 1111.92033Mudassar, Imran; Smith, Hal 10 2006 Multiple limit cycles in the standard model of three species competition for three essential resources. Zbl 1110.92046Baer, Steven M.; Li, Bingtuan; Smith, Hal L. 7 2006 Monotone dynamical systems. Zbl 1094.34003Hirsch, M. W.; Smith, Hal 93 2005 Monotone maps: a review. Zbl 1080.37016Hirsch, M. W.; Smith, Hal 46 2005 Biofilms and the plasmid maintenance question. Zbl 1064.92044Imran, Mudassar; Jones, Don; Smith, Hal 3 2005 Traveling waves in a bio-reactor model. Zbl 1079.35011Smith, Hal L.; Zhao, Xiao-Qiang 17 2004 Generic quasi-convergence for strongly order preserving semiflows: a new approach. Zbl 1074.34042Hirsch, Morris W.; Smith, Hal L. 5 2004 Virus dynamics: a global analysis. Zbl 1035.34045De Leenheer, Patrick; Smith, Hal L. 199 2003 Feedback control for chemostat models. Zbl 1015.92046De Leenheer, Patrick; Smith, Hal 47 2003 Competition in the chemostat: some remarks. Zbl 1132.92341De Leenheer, Patrick; Li, Bingtuan; Smith, Hal L. 17 2003 The Freter model: A simple model of biofilm formation. Zbl 1023.92010Jones, Don; Kojouharov, Hristo V.; Le, Dung; Smith, Hal 16 2003 Competitive and cooperative systems: mini-review. Zbl 1134.92358Hirsch, Morris W.; Smith, Hal L. 15 2003 Competition for essential resources: a brief review. Zbl 1162.92334Smith, Hal L.; Li, Bingtuan 12 2003 Periodic coexistence of four species competing for three essential resources. Zbl 1018.92031Li, Bingtuan; Smith, Hal L. 11 2003 Strong positivity of solutions to parabolic and elliptic equations on nonsmooth domains. Zbl 1072.35503Le, Dung; Smith, Hal 8 2002 Bacterial wall attachment in a flow reactor. Zbl 1017.92034Jones, Don; Kojouharov, Hristo V.; Le, Dung; Smith, Hal 7 2002 Bacterial wall attachment in flow reactor: Mixed culture. Zbl 1027.92028Jones, Don; Kojouharov, Hristo V.; Le, Dung; Smith, Hal 3 2002 Robust persistence for semidynamical systems. Zbl 1042.37504Smith, Hal L.; Zhao, Xiao-Qiang 156 2001 Global dynamics of an SEIR epidemic model with vertical transmission. Zbl 0991.92029Li, Michael Y.; Smith, Hal L.; Wang, Liancheng 114 2001 Chain transitivity, attractivity, and strong repellors for semidynamical systems. Zbl 1129.37306Hirsch, Morris W.; Smith, Hal L.; Zhao, Xiao-Qiang 99 2001 Stable coexistence and bi-stability for competitive systems on ordered Banach spaces. Zbl 1064.47075Smith, H. L.; Thieme, H. R. 24 2001 How many species can two essential resources support? Zbl 0992.92040Li, Bingtuan; Smith, Hal 24 2001 Competitive exclusion in a discrete-time, size-structured chemostat model. Zbl 1056.92059Smith, H. L.; Zhao, X.-Q. 13 2001 Global asymptotic stability of traveling waves in delayed reaction-diffusion equations. Zbl 0941.35125Smith, Hal L.; Zhao, Xiao-Qiang 121 2000 Microbial competition for nutrient and wall sites in plug flow. Zbl 1013.92047Jones, Don A.; Smith, Hal 11 2000 Competition in a chemostat with wall attachment. Zbl 0992.92017Stemmons, Eric D.; Smith, Hal L. 11 2000 Stable periodic orbits for a predator-prey model with delay. Zbl 0997.92035Cavani, Mario; Lizana, Marcos; Smith, Hal L. 9 2000 Microbial growth in a plug flow reactor with wall adherence and cell motility. Zbl 0999.92039Smith, Hal; Zhao, Xiao-Qiang 6 2000 Competition in the periodic gradostat. Zbl 1004.92036Smith, H. L.; Waltman, Paul 2 2000 A semilinear hyperbolic system. Zbl 0971.35048Smith, Hal 1 2000 Effects of random motility on microbial growth and competition in a flow reactor. Zbl 1051.92039Ballyk, Mary; Dung, Le; Jones, Don A.; Smith, Hal L. 74 1999 Perturbation of a globally stable steady state. Zbl 0924.58087Smith, H. L.; Waltman, P. 49 1999 Dynamics of a periodically pulsed bio-reactor model. Zbl 0930.35085Smith, Hal L.; Zhao, Xiao-Qiang 30 1999 A model of microbial growth in a plug flow reactor with wall attachment. Zbl 0980.92034Ballyk, Mary; Smith, Hal 28 1999 Steady states of models of microbial growth and competition with chemotaxis. Zbl 0933.35088Le Dung; Smith, Hal L. 20 1999 Dynamics of competition. Zbl 1002.92564Smith, H. L. 18 1999 Growth in the unstirred chemostat with different diffusion rates. Zbl 0920.35076Le Dung; Smith, Hal L.; Waltman, P. 8 1999 Competition between plasmid-bearing and plasmid-free microorganisms in a chemostat with distinct removal rates. Zbl 0977.92030Li, Bingtuan; Kuang, Yang; Smith, Hal L. 2 1999 Planar competitive and cooperative difference equations. Zbl 0907.39004Smith, H. L. 115 1998 A flow reactor with wall growth. Zbl 0929.92034Ballyk, Mary M.; Smith, Hal L. 3 1998 Global existence of periodic solutions in a class of delayed Gause-type predator-prey systems. Zbl 0872.34047Zhao, Tao; Kuang, Yang; Smith, H. L. 63 1997 The periodically forced Droop model for phytoplankton growth in a chemostat. Zbl 0878.92032Smith, H. L. 16 1997 Complicated dynamics for low-dimensional strongly monotone maps. Zbl 0893.54034Smith, H. L. 4 1997 Competitive exclusion and coexistence for competitive systems on ordered Banach spaces. Zbl 0860.47033Hsu, S. B.; Smith, H. L.; Waltman, Paul 108 1996 A parabolic system modeling microbial competition in an unmixed bio-reactor. Zbl 0865.35017Le Dung; Smith, Hal L. 43 1996 A discrete, size-structured model of microbial growth and competition in the chemostat. Zbl 0884.92029Smith, H. L. 11 1996 Competition in an unstirred multi-dimensional chemostat. Zbl 0934.35074Smith, Hal L.; Waltman, Paul 4 1996 An application of monotone systems theory to a model of microbial competition. Zbl 0858.92030Smith, Hal L. 2 1996 Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems. Zbl 0821.34003Smith, Hal L. 785 1995 The theory of the chemostat. Dynamics of microbial competition. Zbl 0860.92031Smith, Hal L.; Waltman, Paul 466 1995 Asymptotically autonomous semiflows: Chain recurrence and Lyapunov functions. Zbl 0829.34037Mischaikow, Konstantin; Smith, Hal; Thieme, Horst R. 101 1995 Equivalent dynamics for a structured population model and a related functional differential equation. Zbl 0835.34090Smith, Hal L. 7 1995 On the existence and stability of bounded almost periodic and periodic solutions of a singularly perturbed nonautonomous system. Zbl 0835.34071Smith, Hal L. 7 1995 Tridiagonal competitive-cooperative Kolmogorov systems. Zbl 0870.92018Freedman, H. I.; Smith, H. L. 1 1995 Dynamics of competition in the unstirred chemostat. Zbl 0831.92028Hsu, S. B.; Smith, H. L.; Waltman, Paul 35 1994 Stable periodic orbits for a class of three dimensional competitive systems. Zbl 0802.34064Zhu, Hsiu-Rong; Smith, Hal L. 30 1994 Competition for a single limiting resource in continuous culture: The variable-yield model. Zbl 0829.92020Smith, Hal L.; Waltman, Paul 30 1994 A structured population model and a related functional differential equation: Global attractors and uniform persistence. Zbl 0794.34061Smith, Hal L. 20 1994 Existence and uniqueness of global solutions for a size-structured model of an insect population with variable instar duration. Zbl 0810.92022Smith, Hal L. 12 1994 ...and 62 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 4,010 Authors 80 Zhao, Xiao-Qiang 77 Smith, Hal Leslie 60 Wu, Jianhong 59 Chen, Lansun 46 Wang, Feng-Bin 44 Jiang, Jifa 44 Zou, Xingfu 43 Teng, Zhi-dong 40 Li, Wan-Tong 38 Kulenović, Mustafa R. 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