plz solve this problem which is mathematics models (Part 2: Populations Dynamics

Question

plz solve this problem which is mathematics models (Part 2: Populations Dynamics)

3 populations compete for resources. r and z compete with y, but not with each other r(4-2x-y) = dt (a) Find the critical point (e e, e). Use Routh-Hurwitz to show it is unstable (b) Show that the equilibrium (0.Ye,z.) ?s unstable. (c) Show that the equilibrium (e,0, ze) is stable (d) Show that there is no equilibrium (e ye,0) (e) Show that the equilibrium (0.ye.0) ?s stable. (f) All other equilibria are unstable. What does this say about the populations as

Explanation / Answer

At the critical point, the value of the function needs to zero.

Xc(4-2Xc-Yc) = 0

Yc(5-Xc-Yc-Zc) = 0

Zc(6-2Yc-Zc) = 0

As Xc, Yc and Zc are positive

4-2Xc-Yc = 0

Xc= 2 - Yc/2

6 - 2Yc - Zc = 0

Zc = 6 - 2Yc

5-Xc-Yc-Zc = 0

Replacing Xc and Zc in the above equation

5 - (2 - Yc/2) - Yc - (6 - 2Yc) = 0

Yc = 2

Xc = 1

Zc = 2

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.