The Volterra- Lotka system for two competitive species is dx/dt = x(-Ax -By +C) dy/dt=y(-Dx-Ey+F) where x, y>=0 and where the parameters A-F are all positive. a. Can there ever be more than one equilibrium point with both x>0 and y>0 (that is, where the species "coexist in equilibrium")? If so, give an example of values A-F where the species can coexist. If not, why not? b. What conditions on the parameters A-F guarantee that there is at least one equilibrium point with x>0 and y>0?

The Volterra- Lotka system for two competitive species is dx/dt = x(-Ax -By +C) dy/dt=y(-Dx-Ey+F) where x, y>=0 and where the parameters A-F are all positive. a. Can there ever be more than one equilibrium point with both x>0 and y>0 (that is, where the species "coexist in equilibrium")? If so, give an example of values A-F where the species can coexist. If not, why not? b. What conditions on the parameters A-F guarantee that there is at least one equilibrium point with x>0 and y>0?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

The Volterra- Lotka system for two competitive species is

dx/dt = x(-Ax -By +C)

dy/dt=y(-Dx-Ey+F)

where x, y>=0 and where the parameters A-F are all positive.

a. Can there ever be more than one equilibrium point with both x>0 and y>0 (that is, where the species "coexist in equilibrium")? If so, give an example of values A-F where the species can coexist. If not, why not?

b. What conditions on the parameters A-F guarantee that there is at least one equilibrium point with x>0 and y>0?

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