Edit Profile 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 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) Publications by Year all cited Publications top 5 cited Publications 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 0821.34003Smith, Hal L. 704 1995 The theory of the chemostat. Dynamics of microbial competition. Zbl 0860.92031Smith, Hal L.; Waltman, Paul 419 1995 Abstract functional differential equations and reaction-diffusion systems. Zbl 0722.35046Martin, R. H. jun.; Smith, H. L. 255 1990 An introduction to delay differential equations with applications to the life sciences. Zbl 1227.34001Smith, Hal 197 2011 Virus dynamics: a global analysis. Zbl 1035.34045De Leenheer, Patrick; Smith, Hal L. 170 2003 Dynamical systems and population persistence. Zbl 1214.37002Smith, Hal L.; Thieme, Horst R. 168 2011 Robust persistence for semidynamical systems. Zbl 1042.37504Smith, Hal L.; Zhao, Xiao-Qiang 121 2001 Planar competitive and cooperative difference equations. Zbl 0907.39004Smith, H. L. 112 1998 Cooperative systems of differential equations with concave nonlinearities. Zbl 0612.34035Smith, H. L. 106 1986 Global asymptotic stability of traveling waves in delayed reaction-diffusion equations. Zbl 0941.35125Smith, Hal L.; Zhao, Xiao-Qiang 105 2000 Global dynamics of an SEIR epidemic model with vertical transmission. Zbl 0991.92029Li, Michael Y.; Smith, Hal L.; Wang, Liancheng 97 2001 Competitive exclusion and coexistence for competitive systems on ordered Banach spaces. Zbl 0860.47033Hsu, S. B.; Smith, H. L.; Waltman, Paul 95 1996 Asymptotically autonomous semiflows: Chain recurrence and Lyapunov functions. Zbl 0829.34037Mischaikow, Konstantin; Smith, Hal; Thieme, Horst R. 92 1995 Systems of ordinary differential equations which generate an order preserving flow. A survey of results. Zbl 0674.34012Smith, Hal L. 92 1988 Global stability for infinite delay Lotka–Volterra type systems. Zbl 0786.34077Kuang, Y.; Smith, H. L. 90 1993 The Poincaré-Bendixson theorem for monotone cyclic feedback systems. Zbl 0712.34060Mallet-Paret, John; Smith, Hal L. 87 1990 Monotone semiflows generated by functional differential equations. Zbl 0612.34067Smith, Hal 86 1987 Monotone dynamical systems. Zbl 1094.34003Hirsch, M. W.; Smith, Hal 84 2005 Chain transitivity, attractivity, and strong repellors for semidynamical systems. Zbl 1129.37306Hirsch, Morris W.; Smith, Hal L.; Zhao, Xiao-Qiang 83 2001 Infinite subharmonic bifurcation in an SEIR epidemic model. Zbl 0523.92020Schwartz, Ira B.; Smith, H. L. 80 1983 Reaction-diffusion systems with time delays: Monotonicity, invariance, comparison and convergence. Zbl 0709.35059Martin, R. H. jun.; Smith, H. L. 70 1991 The theory of the chemostat. Dynamics of microbial competition. Reprint of the 1995 hardback ed. Zbl 1139.92029Smith, Hal L.; Waltman, Paul 64 2008 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. 64 1999 Competitive coexistence in an oscillating chemostat. Zbl 0467.92018Smith, Hal L. 64 1981 Periodic competitive differential equations and the discrete dynamics of competitive maps. Zbl 0596.34013Smith, Hal L. 63 1986 Global existence of periodic solutions in a class of delayed Gause-type predator-prey systems. Zbl 0872.34047Zhao, Tao; Kuang, Yang; Smith, H. L. 61 1997 Strongly order preserving semiflows generated by functional differential equations. Zbl 0735.34065Smith, Hal L.; Thieme, Horst R. 58 1991 Perturbation of a globally stable steady state. Zbl 0924.58087Smith, H. L.; Waltman, P. 46 1999 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. 42 1996 Feedback control for chemostat models. Zbl 1015.92046De Leenheer, Patrick; Smith, Hal 42 2003 Slowly oscillating periodic solutions of autonomous state-dependent delay equations. Zbl 0774.34054Kuang, Y.; Smith, H. L. 42 1992 Monotone maps: a review. Zbl 1080.37016Hirsch, M. W.; Smith, Hal 42 2005 Convergence for strongly order-preserving semiflows. Zbl 0739.34040Smith, Hal L.; Thieme, Horst R. 39 1991 Periodic solutions of differential delay equations with threshold-type delays. Zbl 0762.34044Smith, H. L.; Kuang, Y. 38 1992 On the asymptotic behavior of a class of deterministic models of cooperating species. Zbl 0607.92023Smith, Hal L. 38 1986 Subharmonic bifurcation in an S-I-R epidemic model. Zbl 0578.92023Smith, H. L. 38 1983 Dynamics of competition in the unstirred chemostat. Zbl 0831.92028Hsu, S. B.; Smith, H. L.; Waltman, Paul 36 1994 Competing subcommunities of mutualists and a generalized Kamke theorem. Zbl 0609.92033Smith, Hal L. 36 1986 Reduction of structured population models to threshold-type delay equations and functional differential equations: A case study. Zbl 0797.92024Smith, Hal L. 34 1993 Multiple stable subharmonics for a periodic epidemic model. Zbl 0529.92018Smith, H. L. 32 1983 Invariant curves for mappings. Zbl 0606.47056Smith, Hal L. 31 1986 Quasi convergence and stability for strongly order-preserving semiflows. Zbl 0704.34054Smith, Hal L.; Thieme, Horst R. 31 1990 On periodic solutions of a delay integral equation modelling epidemics. Zbl 0354.92035Smith, H. L. 29 1977 Dynamics of a periodically pulsed bio-reactor model. Zbl 0930.35085Smith, Hal L.; Zhao, Xiao-Qiang 29 1999 The interaction of steady state and Hopf bifurcations in a two-predator- one-prey competition model. Zbl 0489.92019Smith, Hal L. 29 1982 Stable periodic orbits for a class of three dimensional competitive systems. Zbl 0802.34064Zhu, Hsiu-Rong; Smith, Hal L. 29 1994 Competition for a single limiting resource in continuous culture: The variable-yield model. Zbl 0829.92020Smith, Hal L.; Waltman, Paul 29 1994 Periodic orbits of competitive and cooperative systems. Zbl 0615.34027Smith, Hal L. 28 1986 Monotone semiflows in scalar non-quasi-monotone functional differential equations. Zbl 0719.34123Smith, Hal L.; Thieme, Horst R. 27 1990 Fixed point techniques in a cone with applications. Zbl 0435.47060Gatica, J. A.; Smith, Hal L. 26 1977 Oscillations and multiple steady states in a cyclic gene model with repression. Zbl 0619.92004Smith, Hal 26 1987 On eigenvalue problems for nondifferentiable mappings. Zbl 0389.34019Schmitt, K.; Smith, H. L. 24 1979 Stable coexistence and bi-stability for competitive systems on ordered Banach spaces. Zbl 1064.47075Smith, H. L.; Thieme, H. R. 23 2001 A model of microbial growth in a plug flow reactor with wall attachment. Zbl 0980.92034Ballyk, Mary; Smith, Hal 23 1999 How many species can two essential resources support? Zbl 0992.92040Li, Bingtuan; Smith, Hal 22 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 21 1991 The discrete dynamics of monotonically decomposable maps. Zbl 1118.65057Smith, H. L. 20 2006 Positive solutions and conjugate points for systems of differential equations. Zbl 0379.34015Schmitt, K.; Smith, H. L. 20 1978 Nonmonotone systems decomposable into monotone systems with negative feedback. Zbl 1103.34021Enciso, G. A.; Smith, H. L.; Sontag, E. D. 19 2006 A structured population model and a related functional differential equation: Global attractors and uniform persistence. Zbl 0794.34061Smith, Hal L. 18 1994 Steady states of models of microbial growth and competition with chemotaxis. Zbl 0933.35088Le Dung; Smith, Hal L. 17 1999 Stable periodic solutions for the hypercycle system. Zbl 0729.34032Hofbauer, J.; Mallet-Paret, J.; Smith, H. L. 17 1991 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 Dynamics of competition. Zbl 1002.92564Smith, H. L. 16 1999 The periodically forced Droop model for phytoplankton growth in a chemostat. Zbl 0878.92032Smith, H. L. 16 1997 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. 15 2006 The Freter model: A simple model of biofilm formation. Zbl 1023.92010Jones, Don; Kojouharov, Hristo V.; Le, Dung; Smith, Hal 15 2003 Global dynamics of microbial competition for two resources with internal storage. Zbl 1125.92058Li, Bingtuan; Smith, Hal L. 15 2007 Dynamics of stoichiometric bacteria-algae interactions in the epilimnion. Zbl 1133.92031Wang, Hao; Smith, Hal L.; Kuang, Yang; Elser, James J. 14 2007 Lyapunov exponents and persistence in discrete dynamical systems. Zbl 1175.34067Salceanu, Paul L.; Smith, H. L. 13 2009 Competition in the gradostat: The role of the communication rate. Zbl 0716.92025Smith, Hal; Tang, Betty 13 1989 Global stability for mixed monotone systems. Zbl 1162.39009Smith, H. L. 12 2008 Competitive exclusion in a discrete-time, size-structured chemostat model. Zbl 1056.92059Smith, H. L.; Zhao, X.-Q. 12 2001 An abstract threshold theorem for one parameter families of positive noncompact operators. Zbl 0476.47041Smith, Hal L. 12 1981 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 Competitive and cooperative systems: mini-review. Zbl 1134.92358Hirsch, Morris W.; Smith, Hal L. 12 2003 A resource-based model of microbial quiescence. Zbl 1098.92067Malik, Tufail; Smith, Hal 12 2006 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 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 Competition for essential resources: a brief review. Zbl 1162.92334Smith, Hal L.; Li, Bingtuan 11 2003 Persistence and global stability for a class of discrete time structured population models. Zbl 1306.37099Smith, Hal L.; Thieme, Horst R. 11 2013 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 Competition in a chemostat with wall attachment. Zbl 0992.92017Stemmons, Eric D.; Smith, Hal L. 10 2000 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 Convergence in Lotka-Volterra type diffusive delay systems without dominating instantaneous negative feedbacks. Zbl 0807.35149Kuang, Yang; Smith, Hal L. 9 1993 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. 9 2016 Models of virulent phage growth with application to phage therapy. Zbl 1151.92316Smith, Hal L. 9 2008 Chemostats and epidemics: competition for nutrients/hosts. Zbl 1273.92039Smith, Hal L.; Thieme, Horst R. 9 2013 Persistence in a discrete-time, stage-structured epidemic model. Zbl 1182.92063Salceanu, Paul Leonard; Smith, Hal L. 8 2010 Does dormancy increase fitness of bacterial populations in time-varying environments? Zbl 1142.92045Malik, Tufail; Smith, Hal L. 8 2008 Growth in the unstirred chemostat with different diffusion rates. Zbl 0920.35076Le Dung; Smith, Hal L.; Waltman, P. 8 1999 Convergence in Lotka-Volterra-type delay systems without instantaneous feedbacks. Zbl 0795.34067Kuang, Yang; Smith, Hal L. 8 1993 Equivalent dynamics for a structured population model and a related functional differential equation. Zbl 0835.34090Smith, Hal L. 7 1995 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. 1 2020 Monotone dynamical systems: reflections on new advances & applications. Zbl 1357.34002Smith, Hal L. 7 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. 9 2016 Persistence versus extinction for a class of discrete-time structured population models. Zbl 1347.37126Jin, Wen; Smith, Hal L.; Thieme, Horst R. 4 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. 11 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 3 2012 Global dynamics of the smallest chemical reaction system with Hopf bifurcation. Zbl 1306.92082Smith, Hal L. 1 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 197 2011 Dynamical systems and population persistence. Zbl 1214.37002Smith, Hal L.; Thieme, Horst R. 168 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. 8 2010 Lyapunov exponents and persistence in discrete dynamical systems. Zbl 1175.34067Salceanu, Paul L.; Smith, H. L. 13 2009 Persistence in a discrete-time stage-structured fungal disease model. Zbl 1342.92278Salceanu, Paul Leonard; Smith, Hal L. 4 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 64 2008 Global stability for mixed monotone systems. Zbl 1162.39009Smith, H. L. 12 2008 Models of virulent phage growth with application to phage therapy. Zbl 1151.92316Smith, Hal L. 9 2008 Does dormancy increase fitness of bacterial populations in time-varying environments? Zbl 1142.92045Malik, Tufail; Smith, Hal L. 8 2008 Prevalent behavior of strongly order preserving semiflows. Zbl 1178.37014Enciso, Germán A.; Hirsch, Morris W.; Smith, Hal L. 7 2008 Global dynamics of microbial competition for two resources with internal storage. Zbl 1125.92058Li, Bingtuan; Smith, Hal L. 15 2007 Dynamics of stoichiometric bacteria-algae interactions in the epilimnion. Zbl 1133.92031Wang, Hao; Smith, Hal L.; Kuang, Yang; Elser, James J. 14 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. 20 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. 15 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. 6 2006 Monotone dynamical systems. Zbl 1094.34003Hirsch, M. W.; Smith, Hal 84 2005 Monotone maps: a review. Zbl 1080.37016Hirsch, M. W.; Smith, Hal 42 2005 Biofilms and the plasmid maintenance question. Zbl 1064.92044Imran, Mudassar; Jones, Don; Smith, Hal 2 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. 170 2003 Feedback control for chemostat models. Zbl 1015.92046De Leenheer, Patrick; Smith, Hal 42 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 15 2003 Competitive and cooperative systems: mini-review. Zbl 1134.92358Hirsch, Morris W.; Smith, Hal L. 12 2003 Periodic coexistence of four species competing for three essential resources. Zbl 1018.92031Li, Bingtuan; Smith, Hal L. 11 2003 Competition for essential resources: a brief review. Zbl 1162.92334Smith, Hal L.; Li, Bingtuan 11 2003 Bacterial wall attachment in a flow reactor. Zbl 1017.92034Jones, Don; Kojouharov, Hristo V.; Le, Dung; Smith, Hal 6 2002 Strong positivity of solutions to parabolic and elliptic equations on nonsmooth domains. Zbl 1072.35503Le, Dung; Smith, Hal 6 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 121 2001 Global dynamics of an SEIR epidemic model with vertical transmission. Zbl 0991.92029Li, Michael Y.; Smith, Hal L.; Wang, Liancheng 97 2001 Chain transitivity, attractivity, and strong repellors for semidynamical systems. Zbl 1129.37306Hirsch, Morris W.; Smith, Hal L.; Zhao, Xiao-Qiang 83 2001 Stable coexistence and bi-stability for competitive systems on ordered Banach spaces. Zbl 1064.47075Smith, H. L.; Thieme, H. R. 23 2001 How many species can two essential resources support? Zbl 0992.92040Li, Bingtuan; Smith, Hal 22 2001 Competitive exclusion in a discrete-time, size-structured chemostat model. Zbl 1056.92059Smith, H. L.; Zhao, X.-Q. 12 2001 Global asymptotic stability of traveling waves in delayed reaction-diffusion equations. Zbl 0941.35125Smith, Hal L.; Zhao, Xiao-Qiang 105 2000 Competition in a chemostat with wall attachment. Zbl 0992.92017Stemmons, Eric D.; Smith, Hal L. 10 2000 Stable periodic orbits for a predator-prey model with delay. Zbl 0997.92035Cavani, Mario; Lizana, Marcos; Smith, Hal L. 9 2000 Microbial competition for nutrient and wall sites in plug flow. Zbl 1013.92047Jones, Don A.; Smith, Hal 7 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. 64 1999 Perturbation of a globally stable steady state. Zbl 0924.58087Smith, H. L.; Waltman, P. 46 1999 Dynamics of a periodically pulsed bio-reactor model. Zbl 0930.35085Smith, Hal L.; Zhao, Xiao-Qiang 29 1999 A model of microbial growth in a plug flow reactor with wall attachment. Zbl 0980.92034Ballyk, Mary; Smith, Hal 23 1999 Steady states of models of microbial growth and competition with chemotaxis. Zbl 0933.35088Le Dung; Smith, Hal L. 17 1999 Dynamics of competition. Zbl 1002.92564Smith, H. L. 16 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. 112 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. 61 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 95 1996 A parabolic system modeling microbial competition in an unmixed bio-reactor. Zbl 0865.35017Le Dung; Smith, Hal L. 42 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. 704 1995 The theory of the chemostat. Dynamics of microbial competition. Zbl 0860.92031Smith, Hal L.; Waltman, Paul 419 1995 Asymptotically autonomous semiflows: Chain recurrence and Lyapunov functions. Zbl 0829.34037Mischaikow, Konstantin; Smith, Hal; Thieme, Horst R. 92 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. 6 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 36 1994 Stable periodic orbits for a class of three dimensional competitive systems. Zbl 0802.34064Zhu, Hsiu-Rong; Smith, Hal L. 29 1994 Competition for a single limiting resource in continuous culture: The variable-yield model. Zbl 0829.92020Smith, Hal L.; Waltman, Paul 29 1994 A structured population model and a related functional differential equation: Global attractors and uniform persistence. Zbl 0794.34061Smith, Hal L. 18 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 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. 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