READING LIST

  1. R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and

Control, Oxford University Press (1992).

  1. J. Best, C. Castillo-Chavez and A. Yakubu, Hierarchical competition in discrete time models with dispersal, Fields Institute Communications, 36, 59-86 (2003).
  2. R. J. H. Beverton and S. J. Holt, On the dynamics of exploited fish populations, Fish. Invest. Ser. II, Mar. Fish. G. B. Minist. Agric. Fish Food (1957).
  3. F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer-Verlag, New York (2000)
  4. C. Castillo-Chavez and A. Yakubu, Interplay between local dynamics and dispersal in discrete-time metapopulation models, Journal of Theoretical Biology, 218, 273-288 (2002).
  5. C. Castillo-Chavez et al, Mathematical Approaches For Emerging and Reemerging Infectious Diseases: Models, Methods and Theory, Springer-Verlag, Volume 125, Edited by Carlos Castillo-Chavez with Sally Blower, Pauline van den Driessche, Denise Kirschner and Abdul-Aziz Yakubu (2001).
  6. C. Castillo-Chavez and A. Yakubu, Discrete-time S-I-S models with complex dynamics, Nonlinear Anal.: Theory, Methods and Appl., 47(7), 4753-4762 (2001).
  7. H. Caswell, Matrix Population Models: Construction, Analysis, and Interpretation, Sinauer Associates (2000).
  8. P. Cull, Local and global stability for population models, Biol. Cybern., 54, 141 (1986).
  9. J. M. Cushing, An Introduction to structured population dynamics, CBMS-NSF Regional Conference Series in Applied Mathematics, 71, SIAM, Philadelphia
  10. R. L. Devaney, An Introduction to Chaotic Dynamical Systems, The Benjamin/Cummings Publishing Co. Inc., Menlo Park, CA (1986).
  11. M. Doebeli, Dispersal and dynamics, Theor. Popl. Biol. 47, 82-106 (1995).
  12. L. Edelstein-Keshet, Mathematical Models in Biology, SIAM Classics in

Applied Mathematics (46) (2004).

  1. S. Elaydi and A. Yakubu, Global stability of cycles: Lotka-Volterra competition model with stocking, J. Difference Equations and Appl., 8(6), 537-549 (2002).
  2. M. J. Feigenbaum, The metric universal properties of period doubling bifurcations and the spectrum for a route to turbulence. In Nonlinear Dynamics, R. H. G. Hellenman, ed. Ann. N. Y. Acad. Science, 357, 330-336 (1980).
  3. J. Franke and A. Yakubu, Mutual exclusion versus coexistence in discrete competitive systems, J. Math. Biol. Vol. 30, 161-168 (1991).
  4. J. Franke and A. Yakubu, Population models with periodic recruitment functions and survival rates, Journal of Difference Equations and Appl., 11(14), 1169-1184 (2005).
  5. J. Franke and A. Yakubu, Discrete-time SIS Epidemic Model in a Seasonal Environment, SIAM Journal of Applied Mathematics (In press).
  6. M. P. Hassell, The dynamics of competition and predation, Studies in Biol., 72, The Camelot Press Ltd. (1976).
  7. A. Hastings, Complex interactions between dispersal and dynamics: Lessons from coupled logistic equations, Ecology, 75, 1362-1372 (1976).
  8. M. W. Hirsch and S. Smale, Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press, New York (1974).
  9. P. H. Leslie, On the use of matrices in certain population mathematics, Biometrika, 33: 183-212 (1945).
  10. T. Y. Li and J. A. Yorke, Period three implies chaos, Amer. Math. Monthly, 82, 985-992 (1975).
  11. R. M. May, Simple mathematical models with very complicated dynamics, Nature, 261, 459-469 (1977).
  12. R. M. May, Stability and complexity in model ecosystems, Princeton University Press (1974).
  13. C. Robinson, Dynamical Systems: Stability, Symbolic Dynamics, and Chaos,

CRC Press (2000).

  1. H. Smith, Cooperative systems of ordinary differential equations with concave nonlinearities, Non. Anal. TMA, 10, 1037-1052 (1986).
  2. A. Yakubu, The effects of planting and harvesting endangered species in discrete competitive systems, Math. Biosc. 126:1-20 (1995).
  3. A. Yakubu, Multiple attractors in juvenile-adult single species models, Journal of Difference Equations and Appl., 9(12), 1083-1098 (2003).
  4. A. Yakubu, R. Seinz, J. Stein and L. Jones, Monarch Butterfly Spatially Discrete Advection Model, Math. Biosc., 190, 183-202 (2004).
  5. P. Yodzis, Introduction to Theoretical Ecology, Harper and Row Publishers Inc (1989).

Computer Programs:

  1. Dynamics: Numerical Exploration by Helena E. Nusse & James A. Yorke
  2. Phaser Scientific Software, A Universal Simulator for Dynamical Systems
  3. Matlab