ertain populations that are present in a given habitat and are related in such a way that one species, known as the prey, has an ample food supply and the other species, known as the predator, feeds on the prey. This situation can be modeled with a system of differential equations known as the predator-prey or Lotka-Volterra equations. A solution of this system of equations is a pair of functions R (t ) and V (t) that describe the populations of the prey and predator as functions of time. Usually, it is impossible to find explicit formulas for R and V so graphical methods are used to analyze the equations. (1) Suppose that the populations of aphids and ladybugs are modeled with a system of Lotka- Volterra equations given below dA/dt=2A(1-0.0001A)-0.01AL dL/dt= -.5L+.0001AL where A(t) is the aphid p
part B plz and if possible part C
Certain populations that are present in a given habitat and are related in such a way that one species, known as the prey, has an ample food supply and the other species, known as the predator, feeds on the prey. This situation can be modeled with a system of differential equations known as the predator-prey or Lotka-Volterra equations. A solution of this system of equations is a pair of functions R (t ) and V (t) that describe the populations of the prey and predator as functions of time. Usually, it is impossible to find explicit formulas for R and V so graphical methods are used to analyze the equations.
(1) Suppose that the populations of aphids and ladybugs are modeled with a system of Lotka- Volterra equations given below
dA/dt=2A(1-0.0001A)-0.01AL
dL/dt= -.5L+.0001AL
where A(t) is the aphid population at time t and L(t)is the ladybug population at time t.
a) In the absence of ladybugs, what does the model predict about the aphids?
b) Identify the equilibrium (constant) solutions to the system.
c) Find an expression for dL/dA .
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