3. Two species with population sizes x and y evolve according to the following pair of coupled differential equations: dx = 4x(5- y), dt dy dt =-y(1-x). I (a) [ (b) (c) (d) Briefly explain what kind of system these equations describe and provide an inter- pretation for each of the various terms in these equations. 1 Determine all of the equilibrium points for x, y. Find an approximate solution to these equations near to non-zero equilibrium. Describe the general behaviour of x, y in the four regions I: x1, y <5, II: >1,y>5 III: <1,y> 5, IV: x < 1, y < 5.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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3. Two species with population sizes x and y evolve according to the following pair of coupled
differential equations:
dx
= 4x(5- y),
dt
dy
dt
=-y(1-x). I
(a) [
(b)
(c)
(d)
Briefly explain what kind of system these equations describe and provide an inter-
pretation for each of the various terms in these equations.
1
Determine all of the equilibrium points for x, y.
Find an approximate solution to these equations near to non-zero equilibrium.
Describe the general behaviour of x, y in the four regions
I: x1, y <5, II: >1,y>5 III: <1,y> 5, IV: x < 1, y < 5.
Transcribed Image Text:3. Two species with population sizes x and y evolve according to the following pair of coupled differential equations: dx = 4x(5- y), dt dy dt =-y(1-x). I (a) [ (b) (c) (d) Briefly explain what kind of system these equations describe and provide an inter- pretation for each of the various terms in these equations. 1 Determine all of the equilibrium points for x, y. Find an approximate solution to these equations near to non-zero equilibrium. Describe the general behaviour of x, y in the four regions I: x1, y <5, II: >1,y>5 III: <1,y> 5, IV: x < 1, y < 5.
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