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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.).

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.).

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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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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