The Lotka-Volterra model is often used to characterize predator-prey interactions. For example, if R is the population of rabbits (which reproduce autocatlytically), G is the amount of grass available for rabbit food (assumed to be constant), L is the population of Lynxes that feeds on the rabbits, and D represents dead lynxes, the following equations represent the dynamic behavior of the populations of rabbits and lynxes: R+G→ 2R (1) L+R → 2L (2) (3) Each step is irreversible since, for example, rabbits cannot turn back into grass. a) Write down the differential equations that describe how the populations of rabbits (R) and lynxes (L) change with time. b) Assuming G and all of the rate constants are unity, solve the equations for the evolution of the animal populations with time. Let the initial values of R and L be 20 and 1, respectively. Plot your results and discuss how the two populations are related.
The Lotka-Volterra model is often used to characterize predator-prey interactions. For example, if R is the population of rabbits (which reproduce autocatlytically), G is the amount of grass available for rabbit food (assumed to be constant), L is the population of Lynxes that feeds on the rabbits, and D represents dead lynxes, the following equations represent the dynamic behavior of the populations of rabbits and lynxes: R+G→ 2R (1) L+R → 2L (2) (3) Each step is irreversible since, for example, rabbits cannot turn back into grass. a) Write down the differential equations that describe how the populations of rabbits (R) and lynxes (L) change with time. b) Assuming G and all of the rate constants are unity, solve the equations for the evolution of the animal populations with time. Let the initial values of R and L be 20 and 1, respectively. Plot your results and discuss how the two populations are related.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The Lotka-Volterra model is often used to characterize predator-prey interactions. For example,
if R is the population of rabbits (which reproduce autocatlytically), G is the amount of grass
available for rabbit food (assumed to be constant), L is the population of Lynxes that feeds on
the rabbits, and D represents dead lynxes, the following equations represent the dynamic
behavior of the populations of rabbits and lynxes:
R+G→ 2R (1)
L+R→ 2L (2)
(3)
Each step is irreversible since, for example, rabbits cannot turn back into grass.
a) Write down the differential equations that describe how the populations of rabbits (R) and
lynxes (L) change with time.
b) Assuming G and all of the rate constants are unity, solve the equations for the evolution of
the animal populations with time. Let the initial values of R and L be 20 and 1, respectively.
Plot your results and discuss how the two populations are related.
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