Predatorpreymodel

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Unformatted text preview: he
growth
of
a
single
species
that
lives
alone
in
 an
environment.
 Now,
we
will
consider
two
species
interac:ng
in
 the
same
habitat.
 One
species,
called
the
prey,
has
an
ample
food
 supply
and
the
second
species,
call
the
predator,
 feeds
on
the
prey.

 Predator‐Prey
Model
 For
example,
consider
a
popula:on
of
rabbits
 (prey)
and
wolves
(predators)
in
an
isolated

 forest.
 Let

 R( t ) = # rabbits at time t W ( t ) = # wolves at time t Two
dependent
variables,
 both
func:ons
of
:me
 Predator‐Prey
Model
 Assump&on
1:
 Without
predators,
prey
will
grow
exponen:ally.
 dR = kR, k > 0 dt Without
prey,
predators
will
die
out
exponen:ally.
 € dW = −rW , r > 0 dt Predator‐Prey
Model
 Assump&on
2:
 There
will
be
more
encounters
between
the
two...
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This note was uploaded on 08/13/2013 for the course MATH 1LT3 taught by Professor Erinclements during the Fall '13 term at McMaster University.

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