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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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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