The dynamics of a fish population is described by the Richard's growth law dN (1) dt where N = N(t) is the population size depending on the continuous time variable 1, and r and K are positive constants.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1. The dynamics of a fish population is described by the Richard's growth law
dN
N
(1)
dt
K
where N = N(t) is the population size depending on the continuous time variable 1, and r
and K are positive constants.
Transcribed Image Text:1. The dynamics of a fish population is described by the Richard's growth law dN N (1) dt K where N = N(t) is the population size depending on the continuous time variable 1, and r and K are positive constants.
(ii) Sketch the graph of the function in the right hand side of equation (1) for N 2 0. Use
your sketch to show that the system has a single non-zero equilibrium, determine its
stability and clearly indicate the stability of the steady state on your graph using
arrows.
Transcribed Image Text:(ii) Sketch the graph of the function in the right hand side of equation (1) for N 2 0. Use your sketch to show that the system has a single non-zero equilibrium, determine its stability and clearly indicate the stability of the steady state on your graph using arrows.
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