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Solved: In each of 11 through 14: a. Sketch the nullclines and describe how the critical
Chapter 9, Problem 11(choose chapter or problem)
In each of 11 through 14: a. Sketch the nullclines and describe how the critical points move as increases. b. Find the critical points. G c. Let = 2. Classify each critical point by investigating the corresponding approximate linear system. Draw a phase portrait in a rectangle containing the critical points. G d. Find the bifurcation point 0 at which the critical points coincide. Locate this critical point, and find the eigenvalues of the approximate linear system. Draw a phase portrait. G e. For > 0, there are no critical points. Choose such a value of and draw a phase portrait.x_ = 4x + y + x2, y_ = 32 y 1
Questions & Answers
QUESTION:
In each of 11 through 14: a. Sketch the nullclines and describe how the critical points move as increases. b. Find the critical points. G c. Let = 2. Classify each critical point by investigating the corresponding approximate linear system. Draw a phase portrait in a rectangle containing the critical points. G d. Find the bifurcation point 0 at which the critical points coincide. Locate this critical point, and find the eigenvalues of the approximate linear system. Draw a phase portrait. G e. For > 0, there are no critical points. Choose such a value of and draw a phase portrait.x_ = 4x + y + x2, y_ = 32 y 1
ANSWER:Step 1 of 8
If the Eigen values of differential equations are real and negative, then the critical point is an asymptotically stable node. And if the Eigen values of the given differential equation are real with opposite signs, then the critical point is an unstable saddle point.