2,373
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Mathematical and numerical comparisons of five single-population growth models

Pages 95-103 | Received 19 Aug 2015, Accepted 20 Oct 2015, Published online: 25 Nov 2015

References

  • H.T. Banks and C. Castillo-Chávez (eds), Bioterrorism: Mathematical Modeling Applications in Homeland Security, SIAM, Philadelphia, 2003.
  • S.R. Beissinger and M.I. Westphal, On the use of demographic models of population viability in endangered species management, J. Wildlife Manag. 62 (1998), pp. 821–841.
  • J.M. Borwein and R.M. Carless, Emerging tools for experimental mathematics, Amer. Math. Monthly 106 (1999), pp. 889–909.
  • F. Brauer and C. Castillo-Chávez, Mathematical Models in Population Biology and Epidemiology, Springer, New York, 2001.
  • I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, New York, 1965.
  • F.C. Hoppensteadt and C.S. Peskin, Modeling and Simulation in Medicine and the Life Sciences, 2nd ed., Springer, New York, 2002.
  • S.S. Hsu, S. Hubbell, and P. Waltman, A mathematical theory for single-nutrient competition in continuous cultures of micro-organisms, SIAM J. Appl. Math. 32 (1977), pp. 366–383.
  • H.E. Huntley, Dimensional Analysis, Dover, New York, 1967.
  • G.E. Hutchinson, Introduction to Population Ecology, Yale University Press, New Haven, 1978, Chapter 1.
  • R.E. Mickens, Mathematical Methods for the Natural and Engineering Sciences, World Scientific, London, 2004, Sections 1.3 and 1.4.
  • R.E. Mickens, Wave front behavior of traveling wave solutions for a PDE having square-root dynamics, Math. Compt. Simul. 82 (2012), pp. 1271–1277.
  • R.K. Nagle, E.B. Saff, and A.D. Snider, Fundamentals of Differential Equations, 7th ed., Pearson, Boston, 2008.
  • R.E. O'Malley Jr., Thinking About Ordinary Differential Equations, Cambridge University Press, New York, 1997, Section 6.5.
  • S.L. Ross, Differential Equations, Blaisdell, Waltham, MA, 1964.
  • H.R. Thieme, Mathematics in Population Biology, Princeton University Press, Princeton, 2003, Chapters 5 and 6.
  • C.P. Winsor, The Gompertz curve as a growth curve, Proc. Natl. Acad. Sci. 18 (1932), pp. 1–8.