Suppose that types a and b interact with a fixed population of 500 of the other (set b = 500 in the differential equation for a).
If each state variable in a system of autonomous differential equations does not respond to changes in the value of the other, but depends only on a constant value, the two equations can be considered separately. For example, in the competition equation,

we could treat b as a constant value. In each case, find the equilibrium and draw a phase-line diagrams for a. Set the parameters to μ = 2 and Ka = 1000.

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dt = μ (1-246