A Phase Portrait of a Predator-Prey System Is Given Below

question 120

Essay

A phase portrait of a predator-prey system is given below in which F represents the population of foxes (in thousands) and R the population of rabbits (in thousands). (a) Referring to the graph, what is a reasonable non-zero equilibrium solution for the system?
(b) Write down a possible system of differential equations which could have been used to produce the given graph.(c) Describe how each population changes as time passes, using the initial condition P indicated on the graph.(d) Use your description in part (c) to make a rough sketch of the graph of R and F as functions of time.

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Definitions:

Break-Even Rate

The interest rate at which the present value of a project's or investment's costs equals the present value of its benefits, there is no net loss or gain.

Annuity A

Represents a financial product that promises to pay the holder a fixed stream of payments over a specified period of time.

APR

Annual Percentage Rate, a measure used to calculate the cost of borrowing, including interest and other fees, shown as a yearly rate.

EAR

Ear is the acronym for Effective Annual Rate, which measures the real return on an investment or the real interest rate on a loan, accounting for compounding over a specified period.