The plant model we covered in class is Pn+1 = apn+bpn-1 where a, b > 0....

 

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The plant model we covered in class is Pn+1 = apn+bpn-1 where a, b > 0. As you know, the solution is given by Pn = C₁+C₂A2 where A² = a + b. (a) Find a threshold ac such that the plants go extinct (pn → 0 as n → ∞) when 0 < a < ac, and plants grow exponentially, (pn →∞ as n →∞) when a > ac. Note that ac will depend on b. (b) Suppose that a = ac (with a, b > 0). What is the long-term behaviour (n → ∞) in this case? The plant model we covered in class is Pn+1 = apn+bpn-1 where a, b > 0. As you know, the solution is given by Pn = C₁+C₂A2 where A² = a + b. (a) Find a threshold ac such that the plants go extinct (pn → 0 as n → ∞) when 0 < a < ac, and plants grow exponentially, (pn →∞ as n →∞) when a > ac. Note that ac will depend on b. (b) Suppose that a = ac (with a, b > 0). What is the long-term behaviour (n → ∞) in this case?

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a ac 2b When a ac the plants go extinct because the growth rate is negative When a ac the growth rat... View the full answer