In the competition model for two species with populations N1 and N2 N2 b12 K1 dN1 N1 dt K1 dN2 N1 = 12N2 (1 – b21 dt K2 where only one species, N1, has limited carrying capacity. Nondimensionalise the system and determine the steady states. Investigate their stability and sketch the phase plane trajectories. Show that irrespective of the size of the parameters the principle of competitive exclusion holds. Briefly describe under what ecological cir- cumstances the species N2 becomes extinct.

In the competition model for two species with populations N1 and N2 N2 b12 K1 dN1 N1 dt K1 dN2 N1 = 12N2 (1 – b21 dt K2 where only one species, N1, has limited carrying capacity. Nondimensionalise the system and determine the steady states. Investigate their stability and sketch the phase plane trajectories. Show that irrespective of the size of the parameters the principle of competitive exclusion holds. Briefly describe under what ecological cir- cumstances the species N2 becomes extinct.

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Exercises
1 In the competition model for two species with populations N1 and N2
dN1
N1
= rịN1
dt
N2
- b12-
K1
K1
会).
d N2
N1
= r2N2 (1- b21-
K2,
dt
where only one species, N1, has limited carrying capacity. Nondimensionalise the
system and determine the steady states. Investigate their stability and sketch the
phase plane trajectories. Show that irrespective of the size of the parameters the
principle of competitive exclusion holds. Briefly describe under what ecological cir-
cumstances the species N2 becomes extinct.

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