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3. Consider the following system: dz z(3 -z- 2y), dt dy = y(2 – y - z). dt (a) Find the steady states. (Hint: there are four steady states. ) (b) forget to label the ticks in x-axis and y-axis. Using different colors for x-nullcline and y-nullcline can help you to identify all steady state. ) Sketch the nullelines and label all steady states for the full zy-plane. (Don't (c) coordinates are both positive) and determine the stability for it. Find the corresponding linearized system at the positive steady state (whose

3. Consider the following system: dz z(3 -z- 2y), dt dy = y(2 – y - z). dt (a) Find the steady states. (Hint: there are four steady states. ) (b) forget to label the ticks in x-axis and y-axis. Using different colors for x-nullcline and y-nullcline can help you to identify all steady state. ) Sketch the nullelines and label all steady states for the full zy-plane. (Don't (c) coordinates are both positive) and determine the stability for it. Find the corresponding linearized system at the positive steady state (whose

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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Consider the following system: dr 2(3 –2 - 2y), dt dy = y(2 – y - 2). dt (a) (b) forget to label the ticks in x-axis and y-axis. Using different colors for x-nullcline and y-nullcline can help you to identify all steady state. ) Find the steady states. (Hint: there are four steady states. ) аге Sketch the nullelines and label all steady states for the full ry-plane. (Don't (c) coordinates are both positive) and determine the stability for it. (d) stable spiral, neutral center, unstable spiral) (e) node, stable spiral, neutral center, unstable spiral) Find the corresponding linearized system at the positive steady state (whose Classify the type of the steady state (0,0). (stable node, saddle, unstable node, Classify the type of the positive steady state. (stable node, saddle, unstable 3.
Transcribed Image Text:Consider the following system: dr 2(3 –2 - 2y), dt dy = y(2 – y - 2). dt (a) (b) forget to label the ticks in x-axis and y-axis. Using different colors for x-nullcline and y-nullcline can help you to identify all steady state. ) Find the steady states. (Hint: there are four steady states. ) аге Sketch the nullelines and label all steady states for the full ry-plane. (Don't (c) coordinates are both positive) and determine the stability for it. (d) stable spiral, neutral center, unstable spiral) (e) node, stable spiral, neutral center, unstable spiral) Find the corresponding linearized system at the positive steady state (whose Classify the type of the steady state (0,0). (stable node, saddle, unstable node, Classify the type of the positive steady state. (stable node, saddle, unstable 3.
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