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dx dt dy dt = 2x = 3 3y (1-1)-xy ху 8273 (1 - 1) - 2 - 2xy

dx dt dy dt = 2x = 3 3y (1-1)-xy ху 8273 (1 - 1) - 2 - 2xy

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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6. For the competing species population model dx dt dy = 2x (1 - -/-) - ху = 3y (1-1)-2xy dt studied in this section, we showed that the equilibrium point (1, 1) is a saddle. (a) Find the linearized system near each of the other equilibrium points. (b) Classify each equilibrium point (as either a source, a sink, a saddle, ...). (c) Sketch the phase portrait of each linearized system. (d) Give a brief description of the phase portrait near each equilibrium point of the nonlinear system.
Transcribed Image Text:6. For the competing species population model dx dt dy = 2x (1 - -/-) - ху = 3y (1-1)-2xy dt studied in this section, we showed that the equilibrium point (1, 1) is a saddle. (a) Find the linearized system near each of the other equilibrium points. (b) Classify each equilibrium point (as either a source, a sink, a saddle, ...). (c) Sketch the phase portrait of each linearized system. (d) Give a brief description of the phase portrait near each equilibrium point of the nonlinear system.
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