Math 5110/6830
Instructor: Alla Borisyuk
Homework 5.1
Due: September 29
1. (dV 2.14.17) Suppose that we modify the assumptions of the NicholsonBailey model (that we considered in class) in the following way: if a host has
one encounter with a parasitoid f parasitoid progeny will be produced, but if it
has two or more encounters 2f parasitoid progeny are produced. Write down a
new model incorporating this assumption.
2. One possible modication for the Nicholson-Bailey model is to limit the
growth of the host species in isolation by assuming intra-species competition
and, subsequently, an existence of the carrying capacity (maximum possible
level of the population). Beddington, Free and Lawton realized this in the
following model:
Nn+1 = er(1 Nn =K ) Nn e aPn ;
(1)
P
= fN [1 e aPn ]:
n+1
a)Determine all xed points
b)Under what conditions on
stable?
n
the model parameters are xed points stable? Un-
Can you suggest some other factors that may stabilize the
coexistence solution in Nicholson-Bailey model? You can describe the modications in words or pictures and, perhaps, formulas. You do not need to analyze
these new models.
c)(Extra credit)
1