Question 12. population. The following differential equation describes the dynamics of a x' = x²(2-x) - hx, where h> 0 is the intensity of harvesting. (a) Find all equilibria. [Hint: some of them will depend on h.] (b) For which values of h is there at least one positive equilibrium? (c) For h = 5/9 determine the stability of each equilibrium analytically (not from the phase line diagram).

Question 12. population. The following differential equation describes the dynamics of a x' = x²(2-x) - hx, where h> 0 is the intensity of harvesting. (a) Find all equilibria. [Hint: some of them will depend on h.] (b) For which values of h is there at least one positive equilibrium? (c) For h = 5/9 determine the stability of each equilibrium analytically (not from the phase line diagram).

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.5: Nonlinear Systems Of Differential Equations

Problem 1YT: YOUR TURN Consider the system of differential equations dx1dt=x1x23x1dx2dt=3x1x26x2 a. Find all...

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