3. Consider the Ricker equation: Nn+1 = aN,e-BN, In this equation, a represents the maximal growth rate of the organism and ß is the inhibition of growth caused by overpopulation.

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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3. Consider the Ricker equation:
Nn+1 = aN,e¬BN,.
In this equation, a represents the maximal growth rate of the organism and ß is the inhibition of
growth caused by overpopulation.
(a) Show that this equation has a steady state
In a
Ñ =
(b) Show that the steady state in the first part is stable provided that
|1 – In a| < 1.
-
Transcribed Image Text:3. Consider the Ricker equation: Nn+1 = aN,e¬BN,. In this equation, a represents the maximal growth rate of the organism and ß is the inhibition of growth caused by overpopulation. (a) Show that this equation has a steady state In a Ñ = (b) Show that the steady state in the first part is stable provided that |1 – In a| < 1. -
Expert Solution
Step 1

Given, the Ricker equation:                               Nn+1=αNne-βNn                              ...(1)Where α represents the maximum growth rate of the organism and β is the inhibitaion of growth caused overpopulation.

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