1. A population that grows under limited resources and is preyed on by a predator can be described by a simple single-variable model in non-dimensional form: dd=(1)ab2+22. (a) Interpret the predation term; specifically, how successful is the predator when the prey species is present at low numbers (>b). (b) Treat b as a fixed value but allow a to vary. This means we want to consider a whole collection of possible populations, each having the same b value but a different a value. Find all steady states of the equation for each value of a and plot the steady state values as functions of a. For example, =0 is always a steady state so plot the zero function (i.e. (a)=0 ). There are sometimes other steady states so plot another function for each of those. Suggestion: if you can't solve for ss as a function of a, solve for a as a function of ss and plot that sideways in the -a plane. 1. A population that grows under limited resources and is preyed on by a predator can be described by a simple single-variable model in non-dimensional form: dd=(1)ab2+22. (a) Interpret the predation term; specifically, how successful is the predator when the prey species is present at low numbers (>b). (b) Treat b as a fixed value but allow a to vary. This means we want to consider a whole collection of possible populations, each having the same b value but a different a value. Find all steady states of the equation for each value of a and plot the steady state values as functions of a. For example, =0 is always a steady state so plot the zero function (i.e. (a)=0 ). There are sometimes other steady states so plot another function for each of those. Suggestion: if you can't solve for ss as a function of a, solve for a as a function of ss and plot that sideways in the -a plane