Discuss briefly the significance of each of the three terms in the equation 5x - x - 2xy. (i) Show that the three critical points in the linked system are (0,0). (5,0) and (3,1)
Discuss briefly the significance of each of the three terms in the equation 5x - x - 2xy. (i) Show that the three critical points in the linked system are (0,0). (5,0) and (3,1)
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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Solve q3 =(b) parts i ii,iii and iv plz solve this in maximum one hour if u can't solve this u can reject in one hour so that i can't wait of your answer plz.. That i highlighted
Transcribed Image Text:Question 3
(a) A predator-prey linked system is modelled by the autonomous linear system
dx
dy
dt =x+ 3y and
de =*- 3y
where x(t) represents the population of the prey (in thousands) at time t and y(t)
represents the population of the predator (in thousands) at time t.
i) State the critical point
i) Write down the characteristic equation
i) Solve the characteristic equation
iv) Using your solutions determine the nature and stability of the critical point
Transcribed Image Text:(b)A predator-prey linked system is modelled by the differential equations
dx
dy
= 5x – x? – 2xy and
= 2xy – 6y
dt
dt
where x(t) represents the population of the prey (in thousands) at time t and y(t)
represents the population of the predator (in thousands) at time t.
Discuss briefly the significance of each of the three terms in the equation
= 5x - x? - 2xy.
(ii) Show that the three critical points in the linked system are (0,0). (5,0) and (3,1)
"(i) Use appropriate software to sketch the phase plane diagram for this system with
arrows to indicate the direction of the trajectories (flow) and hence determine the nature
and stability of the remaining critical point.
Discuss whether co-existence is possible for these two populations and, if so, at
what level.
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