Note that there is a typo in the statement of 6.4.4. In the defining differential equations, the first b should be a b_1.

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6. 4. 4 The simplest model is N, = EN, - ON, N. . N . = IN, - b, N, N` a) In what way is this model less realistic than the one considered in the text ?* b) Show that by suitable rescalings of MJ. Nz, and I , the model can be nondimensionalized to * " = x 1 1 - W) . Y' = MP - x ). Find a formula For the dimensionless group p . C ) Sketch the nullclines and vector field for the system in ( 6 ). $) Draw the phase portrait , and comment on the biological implications . ? ) Show that ( almost ) all trajectories are curves at the form play - * = Inv - * * C. (Hint: Derive a differential Equation for de'dy , and separate the variables. ] Which trajectories are not al the stated farm ?"