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seasonal predator - prey system, where the prey growth is dependent on a nutrient source, can be modeled by the system of dimensionless differential equations
seasonal predatorprey system, where the prey growth is dependent on a nutrient
source, can be modeled by the system of dimensionless differential equations
dx
dt x Axy
a x
dy
dt Axy
a x y Byz
b y
dz
dt Byz
b y z
where x represents the nutrient source, y represents the prey population, and z represents
the predator population. The parameters govern the rates at which nutrient are consumed,
as well as measures of the organisms ability to subsist on low levels of nutrients.
For this problem, let A B a and b Use x y
and z
a Solve this system of equations using MATLAB ODE integrators for t in Find
the value of time where the system seems to settle into a steady state, with potentially
predictable cycles of behavior.
b Compare the solution components for two different MATLAB ODE algorithms and the
forward Euler method for systems of equations. Describe differences you see, if any, in
the approximations generated by the methods. What size of the time step is needed for
the forward Euler approximations to be comparable to those generated by MATLAB?
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