dN1 =rN1 dt (1-*) - aN1 N2(1 – exp[-bN1]), K %3D dN2 = -dN2+ N2e(1 – exp[-bN1]), dt
dN1 =rN1 dt (1-*) - aN1 N2(1 – exp[-bN1]), K %3D dN2 = -dN2+ N2e(1 – exp[-bN1]), dt
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
Transcribed Image Text:Exercises
117
Nondimensionalise the system by writing
N1
a N2
V = -
e
= n
K'
T =rt,
B = bK.
= -,
r
r
Determine the nonnegative equilibria and note any parameter restrictions. Discuss
the linear stability of the equilibria. Show that a nonzero N2-population can exist if
B > Bc = - In (1 – 8/a). Briefly describe the bifurcation behaviour as B increases
with 0 < 8/a < 1.
%3D
![1)27 there fš a window of values of k
peiodic solutions are possible. Under what conditions can the system exhibit
a threshold phenomenon?
5 The interaction between two populations with densities N1 and N2 is modelled by
dN1
=rN1
dt
(1-)-
-- aN1 N2(1- exp[-bN1]),
K
dN2
:-dN2 + Nze(1 – exp[-bN1]),
dt
where a, b, d, e, r and K are positive constants. What type of interaction exists
between N1 and N2? What do the various terms imply ecologically?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb101ea81-a4ee-44fc-894d-e42058470a0f%2Fe27815df-5f63-4061-b571-51e2aabe3902%2Fbnz1tho_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1)27 there fš a window of values of k
peiodic solutions are possible. Under what conditions can the system exhibit
a threshold phenomenon?
5 The interaction between two populations with densities N1 and N2 is modelled by
dN1
=rN1
dt
(1-)-
-- aN1 N2(1- exp[-bN1]),
K
dN2
:-dN2 + Nze(1 – exp[-bN1]),
dt
where a, b, d, e, r and K are positive constants. What type of interaction exists
between N1 and N2? What do the various terms imply ecologically?
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