(i) Explain the biological meaning of each parameter in model (5). (ii) Find all nullclines of system (5) and sketch them in the x- y plane, clearly showing the location of the steady states.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter5: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 5CC
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3. Some populations (such as algae and bacteria) produce waste products, which in high
concentrations are toxic to the population itself. A mathematical model for a population
x(1) and a toxic waste product y(t) is
dx
(а - В — Ку)х,
dt
(5)
dy
= yx – ôy,
dt
where a, B, y, 8 and K are positive constants.
Transcribed Image Text:3. Some populations (such as algae and bacteria) produce waste products, which in high concentrations are toxic to the population itself. A mathematical model for a population x(1) and a toxic waste product y(t) is dx (а - В — Ку)х, dt (5) dy = yx – ôy, dt where a, B, y, 8 and K are positive constants.
(i) Explain the biological meaning of each parameter in model (5).
(ii) Find all nullclines of system (5) and sketch them in the x- y plane, clearly showing
the location of the steady states.
Transcribed Image Text:(i) Explain the biological meaning of each parameter in model (5). (ii) Find all nullclines of system (5) and sketch them in the x- y plane, clearly showing the location of the steady states.
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