Practice question · Put in order
Predator–prey populations cycle. Starting from many rabbits, few foxes, order the phases of one full cycle.
- Abundant prey lets the fox population grow
- Prey scarcity starves the fox population down
- With few foxes, the rabbit population recovers
- Many foxes drive the rabbit population down
Hints
- Each population’s rise or fall is driven by the current level of the other.
- Foxes always lag the rabbits: predators respond to prey abundance, not the other way around.
Show the answer
- Abundant prey lets the fox population grow
- Many foxes drive the rabbit population down
- Prey scarcity starves the fox population down
- With few foxes, the rabbit population recovers
Why
Each species chases the other’s state a quarter-cycle behind, producing closed loops in the phase plane rather than settling. Real lynx–hare fur records from the Hudson Bay Company show precisely these lagged oscillations.
Practise Systems of Differential Equations
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