HIV-1 Dynamics in Vivo: Virion Clearance Rate, Infected Cell Life-Span,
and Viral Generation Time,
Alan S. Perelson; Avidan U. Neumann; Martin Markowitz; John M. Leonard;
David D. Ho,
Science, New Series, Vol. 271, No. 5255. (Mar. 15, 1996), pp. 1582-1586.
A Theoretical Framework for Data Analysis of Wind Dispersal of Seeds and Pollen,
Akira Okubo and Simon A. Levin,
Ecology, Vol.70, No. 2, (April 1989), pp 329-338.
Dynamics of starvation in humans,
Baojun Song and Diana M. Thomas,
J. Math. Biol. (2007) 54:27-43.
A Tutorial on Hidden Markov Models and
Selected Applications in Speech Recognition,
LAWRENCE R. RABINER,
PROCEEDINGS OF THE IEEE, VOL. 77, NO. 2, FEBRUARY 1989, 257-286.
Large-scale model of mammalian thalamocortical systems,
Eugene M. Izhikevich and Gerald M. Edelman,
PNAS, March 4, 2008. Vol 105, #9. pg 3593-3598.
The dynamics of a simple laissez-faire model with two predators,
< Abstract > In this paper, we study the dynamics of a laissez-faire predator-prey model with both a specialist and a generalist predator. We analyze the stabilities of equilibria by performing linearized stability analyses. We then reexamine the stability of the equilibrium where the prey and predator coexist by constructing a Lyapunov function. If we hold the generalist predator population constant, treating it as a bifurcation parameter, we show that our model can possess multiple (up to three) limit cycles that surround an equilibrium in the interior of the first quadrant. Our model shows rich dynamics including fold, transcritical, pitchfork, Hopf, cyclic-fold, and Bautin bifurcations as well as heteroclinic connections. If we instead vary the generalist predator population slowly across bifurcations, the model exhibits bursting behavior with alternation between a repetitive spiking phase and a quiescent phase.
Chaos and population control of insect outbreaks,
Robert A. Desharnais, R.F. Costantino, J. M. Cushing, Shandelle M. Henson, and Brian Dennis,
Ecology Letters, (2001) 4 : 229 - 235.
Population dynamics of fox rabies in Europe,
Roy M. Anderson, Helen C. Jackson, Robert M. May, and Anthony M. Smith,
Nature, Volume 289, 26 February 1981: 765-771.