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(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.

(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.

Advanced Engineering Mathematics
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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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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