The following mathematical model is proposed for the interaction of two species: N1 b12N2 K1 b21 N1 ). dN1 %3D IP dN2 dT K1 r2N:(1 – Here all parameters are positive. (a) Which of the following terms best describes the nature of the interaction be- tween these species: predator-prey, competition, symbiosis?

Advanced Engineering Mathematics
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ISBN:9780470458365
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Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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2. The following mathematical model is proposed for the interaction of two species:
nNi (1- Ni
K1
dN1
b12 N2
dT
K1
dN2
r2Na(1 –
b21 N1
dT
K2
Here all parameters are positive.
(a) Which of the following terms best describes the nature of the interaction be-
tween these species: predator-prey, competition, symbiosis?
1
(b) Show that a suitable nondimensionalisation leads to the systemy.
The model is modified to
du
u1(1 – u1 – u2)
dt
duz
dt
ru2(1 – bu).
(c) Determine the steady states of this system, and their stability. .
Transcribed Image Text:2. The following mathematical model is proposed for the interaction of two species: nNi (1- Ni K1 dN1 b12 N2 dT K1 dN2 r2Na(1 – b21 N1 dT K2 Here all parameters are positive. (a) Which of the following terms best describes the nature of the interaction be- tween these species: predator-prey, competition, symbiosis? 1 (b) Show that a suitable nondimensionalisation leads to the systemy. The model is modified to du u1(1 – u1 – u2) dt duz dt ru2(1 – bu). (c) Determine the steady states of this system, and their stability. .
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