- Department of Mathematics and Computer Science
- Emory University
- Atlanta, GA 30322, USA
- Email: waltman@emory.edu

- B.S., St. Louis University, 1952
- M.A., (Philosophy) Baylor University, 1954
- M.A., (Mathematics) University of Missouri, 1960
- Ph.D., University of Missouri, 1962 (with W.R. Utz)

USAF, 1952-57

- Assistant Professor, 1965-1966,
- Associate Professor, 1966-1968,
- Professor, 1968-1983

- Professor 1983-2002,
- Chairman, 1983-1986
- Professor Emeritus 2002-

- University of Alberta, Spring 1973
- Arizona State University, 1978-1979
- University of Utah, Spring 1981
- University of Southern California, 1981-1982

**The Theory of the Chemostat: Dynamics of Microbial Competition**, Cambridge University Press, 1994 (with Hal L. Smith). Japanese Language Edition, 2004**A Second Course in Elementary Differential Equations,**Academic Press, 1986. Reprinted, Dover Publications, 2004.**Competition Models in Population Biology**, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 45, SIAM, 1983.**Deterministic Threshold Models in the Theory of Epidemics**, Springer Lecture Notes in Biomathematics, vol. 1, Heidelberg, 1974.**Nonlinear Two Point Boundary Value Problems**, Academic Press, 1968 (with P. Bailey and L.F. Shampine).## Most Recent Journal Articles

(For a complete list with links click here . Links are operative only if your institution subscribes to the web of science. Full text is journal subscription dependent.)

*A survey of mathematical models of competition with an inhibitor,*Mathematical Biosciences, 187 (2004), 53-91 (with S. B. Hsu) pdf*Divergence criteria for generic planar systems,*SIAM J. Applied Mathematics, 64 (2004) 81-93 (with S.S. Pilyugin) pdf*Multiple limit cycles in the chemostat with variable yield,*Mathematical Biosciences 182 (2003), 151-166 (with S.S. Pilyugin) pdf*Did something change? Thresholds in population models,*in Trends in Nonlinear Analysis, M. Kirkilonis, S. Kroemker, R. Rannacer, F. Tomi, Eds, Springer-Verlag, 2002 (with F. Hoppensteadt) pdf*A mathematical model of a biological arms race with a dangerous prey*, J. Theoretical Biology 218 (2002), 55-70 (with J. Braselton and L. Braselton) pdf*A model of the effect of anti-competitor toxins on plasmid-bearing, plasmid-free competition,*Taiwanese J. Mathematics 6 (2002), 135-155 (with S.B. Hsu) pdf*A competition model with dynamically allocated inhibitor production,*Mathematical Biosciences 173 (2001), 55-84 (with J. P. Braselton) pdf*Competition in the presence of a lethal external inhibitor,*Mathematical Biosciences 167 (2000), 177-199 (with S.B. Hsu and Y-S. Li)*Competition in the periodic gradostat,*Nonlinear Analysis, Real World Applications 1 (2000) 177-188 (with H. L. Smith)*Competition in the unstirred chemostat with periodic input and washout,*SIAM Journal on Applied Mathematics 59 (1999), 1157-1177 (with S.S. Pilyugin)*The simple chemostat with wall growth,*SIAM Journal on Applied Mathematics 59 (1999), 1552-1576 (with S.S. Pilyugin)*Growth in the unstirred chemostat with different diffusion rates,*Fields Institute Communications, 21 (1999), 131-142 (with Le Dung and H. L. Smith) pdf*Perturbation of a globally stable steady state,*Proceedings of the American Mathematical Society, 127 (1999), 447-453 (with H. L. Smith)## Most Cited Journal Articles

*Mathematical theory for single nutrient competition in continuous cultures of microorganisms*, SIAM J. Applied Math. 32 (1977), 266-383 (with S.B. Hsu and S. Hubbell) pdf*Uniformly persistent systems*, Proc. Am. Math. Soc . 96 (1986), 425-430 (with G. Butler and H.I. Freedman) pdf*Persistence in models of three interacting predator-prey populations*, Math. Biosciences 68 (1984) 213-231 (with H. I. Freedman) pdf*Singular nonlinear boundary value problems for second order ordinary differential equations,*J. Differential Equations 79 (1989), 62-78 (with J. A. Gatica and V. Oliker) pdf*Persistence in dynamical systems,*J. Differential Equations 63 (1986), 255-263 (with G. Butler) pdf*Persistence in infinite dimensional systems*, SIAM J. Math. Analysis 20 (1989), 388-395 (with J. K. Hale) pdf## Ph.D. Theses Directed

**R. Grimmer**, Almost Autonomous Differential Equations, 1967**J. Heidel**, Qualitative Behavior of Solutions of Nonlinear Third Order Differential Equations, 1967**K. Swick**, Stability and Boundedness Theorems for Third and Fourth Order Nonlinear Differential Equations, 1967**R. Schlunt**, Some Boundary Value Problems for Nonlinear Second Order Differential Equations, 1968**R. Fennell**, Some Boundary Value Problems for Functional Differential Equations, 1969**S.B. Hsu**, A Mathematical Analysis of Competition for a Single Resource, 1976**H. L. Smith**, On Periodic Solutions of Delay Integral Equations Modeling Epidemics and Population Growth, 1976**S. Merrill**, A Mathematical Model of B-cell Stimulation and Humoral Immune Response, 1977**W. Grasman**, Periodic Solutions of Autonomous Differential Equations in Higher Dimensional Spaces, 1977**K. Beck**, Mathematical Models of Population Interactions in Biology, 1980**G. Gersdorff**, Singular Nonlinear Second Order Boundary Value Problems, 1991**S. Ellermeyer**, Delayed Growth Response in Models of Microbial Growth and Competition in Continuous Culture, 1991**R. Pennington**, A Risk Based Model of the Effect of Cofactors on the Spread of the Acquired Immunodeficiency Syndrome, 1993**S. Pilyugin**, Two Models of a Chemostat, 1997