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March  2016, 21(2): i-ii. doi: 10.3934/dcdsb.2016.21.2i

Special issue dedicated to the memory of Paul Waltman

Sze-Bi Hsu 1, , Hal L. Smith 2, and  Xiaoqiang Zhao 3,

1. 

Department of Mathematics, National Tsing Hua University, National Center of Theoretical Science, Hsinchu 300
2. 

School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804
3. 

Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, Canada

Published  November 2015

This volume is dedicated to the memory of Paul Waltman. Many of the authors of articles contained here were participants at the NCTS International Conference on Nonlinear Dynamics with Applications to Biology held May 28-30, 2014 at National Tsing-Hua University, Hsinchu, Taiwan. The purpose of the conference was to survey new developments in nonlinear dynamics and its applications to biology and to honor the memory of Professor Paul Waltman for his influence on the development of Mathematical Biology and Dynamical Systems. Attendees at the conference included Paul's sons Fred and Dennis, many of Paul's former doctoral and post-doctoral students, many others who, although not students of Paul, nevertheless were recipients of Paul's valuable advice and council, and many colleagues from all over the world who were influenced by Paul's mathematics and by his personality. We thank the NCTS for its financial support of the conference and Dr. J.S.W. Wong for supporting the conference banquet.

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Citation: Sze-Bi Hsu, Hal L. Smith, Xiaoqiang Zhao. Special issue dedicated to the memory of Paul Waltman. Discrete & Continuous Dynamical Systems - B, 2016, 21 (2) : i-ii. doi: 10.3934/dcdsb.2016.21.2i
References:
[1]

P. B. Bailey, L. F. Shampine and P. Waltman, Nonlinear two Point Boundary Value Problem,, Math. in Science and Engineering, (1968).   Google Scholar

[2]

G. Butler, H. I. Freedman and P. Waltman, Uniformly persistent systems,, Proc. Amer. Math. Soc., 96 (1986), 425.  doi: 10.1090/S0002-9939-1986-0822433-4.  Google Scholar

[3]

G. Butler and P. Waltman, Persistence in dynamical systems,, J. Diff. Eqns., 63 (1986), 255.  doi: 10.1016/0022-0396(86)90049-5.  Google Scholar

[4]

J. K. Hale and P. Waltman, Persistence in infinite dimensional systems,, SIAM J. Math. Anal., 20 (1989), 388.  doi: 10.1137/0520025.  Google Scholar

[5]

S. R. Hansen and S. P. Hubbell, Single nutrient microbial competition: Agreement between experiment and theoretical forecast outcomes,, Science, 207 (1980), 1491.   Google Scholar

[6]

S. B. Hsu, S. P. Hubbell and P. Waltman, A mathematical theory for single nutrient competition in continuous cultures of micro-organisms,, SIAM J. Appl. Math., 32 (1977), 366.  doi: 10.1137/0132030.  Google Scholar

[7]

P. Waltman, A brief survey of persistence in dynamical systems,, Delay differential equations and dynamical systems (Claremont, (1990), 31.  doi: 10.1007/BFb0083477.  Google Scholar

[8]

P. Waltman, Deterministic Threshold Models in the Theory of Epidemics,, Lecture Notes in Biomathematics, (1974).   Google Scholar

[9]

H. L. Smith and P. Waltman, The Theory of the Chemostat,, Cambrige Univertsity Press, (1995).  doi: 10.1017/CBO9780511530043.  Google Scholar

[10]

P. Waltman, Competition Models in Population Biology,, CBMS-NSF Regional Conference Series in Applied Mathematics, (1983).  doi: 10.1137/1.9781611970258.  Google Scholar

show all references

References:
[1]

P. B. Bailey, L. F. Shampine and P. Waltman, Nonlinear two Point Boundary Value Problem,, Math. in Science and Engineering, (1968).   Google Scholar

[2]

G. Butler, H. I. Freedman and P. Waltman, Uniformly persistent systems,, Proc. Amer. Math. Soc., 96 (1986), 425.  doi: 10.1090/S0002-9939-1986-0822433-4.  Google Scholar

[3]

G. Butler and P. Waltman, Persistence in dynamical systems,, J. Diff. Eqns., 63 (1986), 255.  doi: 10.1016/0022-0396(86)90049-5.  Google Scholar

[4]

J. K. Hale and P. Waltman, Persistence in infinite dimensional systems,, SIAM J. Math. Anal., 20 (1989), 388.  doi: 10.1137/0520025.  Google Scholar

[5]

S. R. Hansen and S. P. Hubbell, Single nutrient microbial competition: Agreement between experiment and theoretical forecast outcomes,, Science, 207 (1980), 1491.   Google Scholar

[6]

S. B. Hsu, S. P. Hubbell and P. Waltman, A mathematical theory for single nutrient competition in continuous cultures of micro-organisms,, SIAM J. Appl. Math., 32 (1977), 366.  doi: 10.1137/0132030.  Google Scholar

[7]

P. Waltman, A brief survey of persistence in dynamical systems,, Delay differential equations and dynamical systems (Claremont, (1990), 31.  doi: 10.1007/BFb0083477.  Google Scholar

[8]

P. Waltman, Deterministic Threshold Models in the Theory of Epidemics,, Lecture Notes in Biomathematics, (1974).   Google Scholar

[9]

H. L. Smith and P. Waltman, The Theory of the Chemostat,, Cambrige Univertsity Press, (1995).  doi: 10.1017/CBO9780511530043.  Google Scholar

[10]

P. Waltman, Competition Models in Population Biology,, CBMS-NSF Regional Conference Series in Applied Mathematics, (1983).  doi: 10.1137/1.9781611970258.  Google Scholar

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