Consider the following model for a host population, with density h(t), and parasite population, with ensity p(t): dh dt Here a₁, a2, b₁, C₁, C₂ are positive constants. i) Interpret each of the terms on the right hand side of these equations (i.e. a₁h etc.) in turn, giving a physical meaning to each. = (a₁-bih-c₁p)h, dp dt = (-a₂ + c₂h)p. (ii) Determine all mathematical possibilities for critical points for this system. You should express one of these points in terms of D = a₁c₂-b₁a₂. (iii) By computing eigenvalues of the relevant Jacobian matrix, analyse the stability of all of the critical points identified in (ii) and hence classify each of them. You should consider the two possibilities D > 0
Consider the following model for a host population, with density h(t), and parasite population, with ensity p(t): dh dt Here a₁, a2, b₁, C₁, C₂ are positive constants. i) Interpret each of the terms on the right hand side of these equations (i.e. a₁h etc.) in turn, giving a physical meaning to each. = (a₁-bih-c₁p)h, dp dt = (-a₂ + c₂h)p. (ii) Determine all mathematical possibilities for critical points for this system. You should express one of these points in terms of D = a₁c₂-b₁a₂. (iii) By computing eigenvalues of the relevant Jacobian matrix, analyse the stability of all of the critical points identified in (ii) and hence classify each of them. You should consider the two possibilities D > 0
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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the other possibility is D<0 parts i to iii would be appreciated
Transcribed Image Text:Consider the following model for a host population, with density h(t), and parasite population, with
ensity p(t):
dh
dt
Here a₁, a2, b₁, C₁, C₂ are positive constants.
i) Interpret each of the terms on the right hand side of these equations (i.e. a₁h etc.) in turn, giving
a physical meaning to each.
=
(a₁-bih-c₁p)h,
dp
dt
= (-a₂ + c₂h)p.
(ii) Determine all mathematical possibilities for critical points for this system. You should express one
of these points in terms of D = a₁c₂-b₁a₂.
(iii) By computing eigenvalues of the relevant Jacobian matrix, analyse the stability of all of the critical
points identified in (ii) and hence classify each of them. You should consider the two possibilities D > 0
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