5. Okay, time for some mathematics. We're going to focus on the interactions between the haresand their main predators, the lynx. The tool we need is differential equations (last seen whenwe talked about the S-I-R disease model). We will let H(t) be the density of hares at time t,and L(t) the density of lynx at time t.Our first assumption is that, if there are no lynx around, the hares grow exponentially. Hareslead to more hares and faster growth. This gives us the differential equation (trust me):HP= aHdtwhere a is a positive constant.Second we assume that, if there are no hares around, the lynx starve and thus their numbersdecay exponentially. This gives us:TP= -bLdt However, there are likely both lynx and hares around at the same time. We will modelinteractions between lynx and hare with a term using H · L in each equation. Our new systemof equations is:НР= aH – cHLdtTP-bL + dHLdtwhere all of a, b, c, d are positive constants.Explain why, in terms of hares and lynx, there is a minus c and a plus d.

Given a system of equations dHdt=aH-cHLdLdt=-bL+dHL where a,b,c,d are positive constants.

However, there are likely both lynx and hares around at the same time. We will model interactions between lynx and hare with a term using H - L in each equation. Our new system of equations is: dH = aH – cHL dt TP -bL + dHL dt where all of a, b, c, d are positive constants. Explain why, in terms of hares and lynx, there is a minus c and a plus d.

However, there are likely both lynx and hares around at the same time. We will model interactions between lynx and hare with a term using H - L in each equation. Our new system of equations is: dH = aH – cHL dt TP -bL + dHL dt where all of a, b, c, d are positive constants. Explain why, in terms of hares and lynx, there is a minus c and a plus d.

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

5. Okay, time for some mathematics. We're going to focus on the interactions between the hares
and their main predators, the lynx. The tool we need is differential equations (last seen when
we talked about the S-I-R disease model). We will let H(t) be the density of hares at time t,
and L(t) the density of lynx at time t.
Our first assumption is that, if there are no lynx around, the hares grow exponentially. Hares
lead to more hares and faster growth. This gives us the differential equation (trust me):
HP
= aH
dt
where a is a positive constant.
Second we assume that, if there are no hares around, the lynx starve and thus their numbers
decay exponentially. This gives us:
TP
= -bL
dt

However, there are likely both lynx and hares around at the same time. We will model
interactions between lynx and hare with a term using H · L in each equation. Our new system
of equations is:
НР
= aH – cHL
dt
TP
-bL + dHL
dt
where all of a, b, c, d are positive constants.
Explain why, in terms of hares and lynx, there is a minus c and a plus d.

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