Exploitation Model System.
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Please help me with these questions.
Given an exploitation model system:
a) nondimensionalize the system
b) find an equilibrium point
c) perform a linear perturbation analysis of the equilibrium point.
d) represent the loci graphically
e) sketch a graph
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Solution Summary
In this solution we find characteristics of and analyze an exploitation model system. It includes a response to a), b), d), & e). This solution includes a pdf file attachment.
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** Please see the attached file for the complete solution **
Solution to a):
Replace each term in the original equation with its equivalent from the dimensionless variables.
For example, H= H/K --> H= HK and dH/dt= dHK/dt=K dH/dt but we need dH/dt for the dimensionless equation.
Using Chain Rule, dH/dt=dH/dt*dt/dt thus,
dH/dt= K dH/dt
=K dH/dt*dt/dt
=K dH/dt*r_1
So now we just need an equivalent expression for P, use P= P/phi*K. ...
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