For each of the systems in Exercises 1-8, perform each of the following tasks. (i) Sketch the nullclines for each equation. Use a distinctive marking for each nullcline so they can be distinguished. (ii) Use analysis to find the equilibrium points for the sys- tem. Label each equilibrium point on your sketch with its coordinates. (iii) Use the Jacobian to classify each equilibrium point (spiral source, nodal sink, etc.).

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 25EQ
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Differential Eqautions

For each of the systems in Exercises 1-8, perform each of the
following tasks.
(i) Sketch the nullclines for each equation. Use a distinctive
marking for each nullcline so they can be distinguished.
(ii) Use analysis to find the equilibrium points for the sys-
tem. Label each equilibrium point on your sketch with its
coordinates.
(iii) Use the Jacobian to classify each equilibrium point (spiral
source, nodal sink, etc.).
4. x' = 2x(1-x/2) - xy
y' = 4y(1-y/4) - 4xy
Transcribed Image Text:For each of the systems in Exercises 1-8, perform each of the following tasks. (i) Sketch the nullclines for each equation. Use a distinctive marking for each nullcline so they can be distinguished. (ii) Use analysis to find the equilibrium points for the sys- tem. Label each equilibrium point on your sketch with its coordinates. (iii) Use the Jacobian to classify each equilibrium point (spiral source, nodal sink, etc.). 4. x' = 2x(1-x/2) - xy y' = 4y(1-y/4) - 4xy
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