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January 29, 2008 8:43 Journal of Biological Dynamics revisionjan Journal of Biological Dynamics

Summary: January 29, 2008 8:43 Journal of Biological Dynamics revisionjan
Journal of Biological Dynamics
Vol. 00, No. 00, Month-Month 200x, 113
Dynamics of a plant-herbivore model
Yun Kang, Dieter Armbruster and Yang Kuang
(Received 00 Month 200x; revised 00 Month 200x; in final form 00 Month 200x)
We formulate a simple host-parasite type model to study the interaction of certain plants and herbivores. Our two dimensional discrete
time model utilizes leaf and herbivore biomass as state variables. The parameter space consists of the growth rate of the host population
and a parameter describing the damage inflicted by herbivores. We present insightful bifurcation diagrams in that parameter space.
Bistability and a crisis of a strange attractor suggest two control strategies: Reducing the population of the herbivore under some
threshold or increasing the growth rate of the plant leaves.
Keywords: Host-parasite model, plant-herbivore model, bifurcation, chaos, control strategies.
AMS Subject Classification: 34K20, 92C50, 92D25.
1. Introduction
The usual framework for discrete-generation host-parasite models has the form
Pn+1 = Pnf(Pn, Hn), (1)
Hn+1 = cPn [1 - f(Pn, Hn)] , (2)
where P and H are the population biomasses of the host (a plant) and the parasite (a herbivore) in
successive generations n and n + 1 respectively, is the host's inherent rate of increase ( = er where r is
the intrinsic rate of increase) in the absence of the parasites, c is the biomass conversion constant, and f


Source: Armbruster, Dieter - Department of Mathematics and Statistics, Arizona State University


Collections: Mathematics