The population model given by the equation: dn = f(n) = -n5 + 10n* – 35n³ + 50n² – 24ne dt The equilibrium points are no = 0,n = 1, n2 = 2, n3 = 3,n4 = 4.“ Plot graphs of the numerical solutions that emanate from initial values situated midway %3D between the respective equilibrium points. Can you explain why certain solution trajectories seem to move faster towards certain stable equilibrium points than others? (Hint: Using Taylor expansion of a function f(n) about a point n = no to consider the approximate form of the solution close to an equilibrium point.)
The population model given by the equation: dn = f(n) = -n5 + 10n* – 35n³ + 50n² – 24ne dt The equilibrium points are no = 0,n = 1, n2 = 2, n3 = 3,n4 = 4.“ Plot graphs of the numerical solutions that emanate from initial values situated midway %3D between the respective equilibrium points. Can you explain why certain solution trajectories seem to move faster towards certain stable equilibrium points than others? (Hint: Using Taylor expansion of a function f(n) about a point n = no to consider the approximate form of the solution close to an equilibrium point.)
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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Transcribed Image Text:The population model given by the equation:
dn
= f(n) = -n5 + 10n* – 35n³ + 50n² – 24ne
dt
The equilibrium points are no = 0,nį = 1, n2 = 2,n3 = 3, n4 = 4.4
%3D
%3D
Plot graphs of the numerical solutions that emanate from initial values situated midway
between the respective equilibrium points. Can you explain why certain solution trajectories
seem to move faster towards certain stable equilibrium points than others?
(Hint: Using Taylor expansion of a function f(n) about a point n = no to consider the
approximate form of the solution close to an equilibrium point.)
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