Solution

ID: past-exam-of-the-topics-in-applied-mathematics-course-of-the-university-of-oxford/2008/a/1/c/ii/solution

With three distinct positive roots of an equation, the negative-leading cubic polynomial has the sign pattern
Equivalently its derivative is negative at the first root of an equation, positive at the middle root of an equation, and negative at the final root of an equation. The phase line arrows therefore point toward the two outer equilibrium points and away from the middle one:
The middle equilibrium point separates the two basin of attraction in the bistability mathematical model parameter interval.

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