![[SBDx] Which of the following differential equations with real parameter u matches the bifurcation diagram in the figure belo](http://img.homeworklib.com/questions/44b19c30-cabf-11ea-980a-f32308d36956.png?x-oss-process=image/resize,w_560)
Homework Answers
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In fiqure , we have unstable for upper part ...
so factor (x-2) is in differential equation...
so we have only 3 options present ...
now as we move value of nu , only 4th option satisfy the property that between small region stable and then below again unstable...
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so answer = 4TH option ....
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[SBDx] Which of the following differential equations with real parameter u matches the bifurcation diagram in...
[SBDu] Which of the following differential equations with real parameter u matches the bifurcation diagram in...
[SBDu] Which of the following differential equations with real parameter u matches the bifurcation diagram in the figure below? Thin blue lines indicate unstable states, thick red lines indicate stable states. 20 -15 -10 -5 ο μ 5 10 15 : Ο α' = (2 – α) (( – 1)? – (μ – 3)) Ο α' = (x – 2) ((α + 1)? – (μ – 3)) Ο α' = (x – 2) (α - 1)? – (μ – 3))...
Nonlinear differential equations and Bifurcation theory. Given the ordinary differential equation =1+re+ where the parameter r...
Nonlinear differential equations and Bifurcation
theory.
Given the ordinary differential equation =1+re+ where the parameter r is a given real number. (a) Sketch all the qualitatively different vector fields that occur as r is varied. (b) Show that a saddle-node bifurcation occurs at a critical value of r, to be determined. (c) Sketch the bifurcation diagram of fixed points r* versus r.
2(a) Consider the one-parameter family of nonlinear ordinary differential equations -Ita-) where ...
2(a) Consider the one-parameter family of nonlinear ordinary differential equations -Ita-) where a is a real parameter. i. Find all equilibrium points. ii. Sketch the bifurcation diagram, and indicate the behaviour of non- equilibrium solutions using appropriate arrows. ii. Find all bifurcation points and classify them
2(a) Consider the one-parameter family of nonlinear ordinary differential equations -Ita-) where a is a real parameter. i. Find all equilibrium points. ii. Sketch the bifurcation diagram, and indicate the behaviour of non- equilibrium...
A bifurcation occurs where the number of equilibrium solutions changes as the parameter varies. As 8...
A bifurcation occurs where the number of equilibrium solutions changes as the parameter varies. As 8 increases, the number of equilibrium solutions changes from two to one and eventually there are none. 4. Solve the equation 0 = yd – 2y + Bfor y in terris of B. Describe how the number of solutions depends on B. 5. Sketch the bifurcation diagram, which shows the graph of y versus 8. It is traditional to show stable equilibria with solid lines...
4) Given the first order equation x'= [lx-x where x = x(t) and u is a...
4) Given the first order equation x'= [lx-x where x = x(t) and u is a real parameter. a) Find all fixed points for u0 and determine whether they are stable or unstable. b) Find all fixed points for u<0 and determine whether they are stable or unstable. c) Sketch the bifurcation diagram for this equation. Be sure to indicate the direction of flow on your diagram (with arrows). This is called a "pitchfork bifurcation" for obvious reasons.
1. Consider the family of differential equations dy/dx = y^3 + ky + k^3 . Please...
1. Consider the family of differential equations dy/dx = y^3 +
ky + k^3 .
Please Help me with it, thanks so much
1. Consider the family of differential equations de set = y2 + ky + k3. (a) Are there any equilibrium solutions when k = 0? If so, what are they? (b) Draw the bifurcation diagram. That is, sketch a graph of the critical values as a function of the parameter k. Clearly label the axes. (You may...
1. Consider the family of differential equations done = y2 + ky + kº. (a) Are...
1. Consider the family of differential equations done = y2 + ky + kº. (a) Are there any equilibrium solutions when k =0? If so, what are they? (b) Draw the bifurcation diagram. That is, sketch a graph of the critical values as a function of the parameter k. Clearly label the axes. (You may use Mathematica for this problem, but your final answer must be drawn by hand.) (c) Draw the phase diagram for when k = -1. For...
3. Each of the following families of differential equations depends on a parameter a. Sketch the ...
3. Each of the following families of differential equations depends on a parameter a. Sketch the corresponding bifurcation diagrams. (a) xx2 -ax (b) x'=x3-ax (c) x' = x, x + a
3. Each of the following families of differential equations depends on a parameter a. Sketch the corresponding bifurcation diagrams. (a) xx2 -ax (b) x'=x3-ax (c) x' = x, x + a
Section B - Answer any two questions. 2. (a) Consider the one-parameter family of nonlinear ordin...
Section B - Answer any two questions. 2. (a) Consider the one-parameter family of nonlinear ordinary differential equations dr where a is a real parameter. i. Find all equilibrium points. ii. Sketch the bifurcation diagram, and indicate the behaviour of non- equilibrium solutions using appropriate arrows. ii. Find all bifurcation points and classify them. 10 Marks (b) Consider the second order differential equation i. Show that (1) can be written as the system of ordinary differential equations (y R for...
For each problem, sketch all of the qualitatively different vector fields that occur as the parameter...
For each problem, sketch all of the qualitatively different vector fields that occur as the parameter u is varied. Find the values of u at which bifurcation occur, and classify the bifurcations. Finally, sketch the bifurcation diagram or the steady states x* vs the parameter u. 1. ** = 5 – ļe-x? 2. espe= ux - T H > 0.
[SBDu] Which of the following differential equations with real parameter u matches the bifurcation diagram in the figure below? Thin blue lines indicate unstable states, thick red lines indicate stable states. 20 -15 -10 -5 ο μ 5 10 15 : Ο α' = (2 – α) (( – 1)? – (μ – 3)) Ο α' = (x – 2) ((α + 1)? – (μ – 3)) Ο α' = (x – 2) (α - 1)? – (μ – 3))...
Nonlinear differential equations and Bifurcation
theory.
Given the ordinary differential equation =1+re+ where the parameter r is a given real number. (a) Sketch all the qualitatively different vector fields that occur as r is varied. (b) Show that a saddle-node bifurcation occurs at a critical value of r, to be determined. (c) Sketch the bifurcation diagram of fixed points r* versus r.
2(a) Consider the one-parameter family of nonlinear ordinary differential equations -Ita-) where a is a real parameter. i. Find all equilibrium points. ii. Sketch the bifurcation diagram, and indicate the behaviour of non- equilibrium solutions using appropriate arrows. ii. Find all bifurcation points and classify them
2(a) Consider the one-parameter family of nonlinear ordinary differential equations -Ita-) where a is a real parameter. i. Find all equilibrium points. ii. Sketch the bifurcation diagram, and indicate the behaviour of non- equilibrium...
A bifurcation occurs where the number of equilibrium solutions changes as the parameter varies. As 8 increases, the number of equilibrium solutions changes from two to one and eventually there are none. 4. Solve the equation 0 = yd – 2y + Bfor y in terris of B. Describe how the number of solutions depends on B. 5. Sketch the bifurcation diagram, which shows the graph of y versus 8. It is traditional to show stable equilibria with solid lines...
4) Given the first order equation x'= [lx-x where x = x(t) and u is a real parameter. a) Find all fixed points for u0 and determine whether they are stable or unstable. b) Find all fixed points for u<0 and determine whether they are stable or unstable. c) Sketch the bifurcation diagram for this equation. Be sure to indicate the direction of flow on your diagram (with arrows). This is called a "pitchfork bifurcation" for obvious reasons.
1. Consider the family of differential equations dy/dx = y^3 +
ky + k^3 .
Please Help me with it, thanks so much
1. Consider the family of differential equations de set = y2 + ky + k3. (a) Are there any equilibrium solutions when k = 0? If so, what are they? (b) Draw the bifurcation diagram. That is, sketch a graph of the critical values as a function of the parameter k. Clearly label the axes. (You may...
1. Consider the family of differential equations done = y2 + ky + kº. (a) Are there any equilibrium solutions when k =0? If so, what are they? (b) Draw the bifurcation diagram. That is, sketch a graph of the critical values as a function of the parameter k. Clearly label the axes. (You may use Mathematica for this problem, but your final answer must be drawn by hand.) (c) Draw the phase diagram for when k = -1. For...
3. Each of the following families of differential equations depends on a parameter a. Sketch the corresponding bifurcation diagrams. (a) xx2 -ax (b) x'=x3-ax (c) x' = x, x + a
3. Each of the following families of differential equations depends on a parameter a. Sketch the corresponding bifurcation diagrams. (a) xx2 -ax (b) x'=x3-ax (c) x' = x, x + a
Section B - Answer any two questions. 2. (a) Consider the one-parameter family of nonlinear ordinary differential equations dr where a is a real parameter. i. Find all equilibrium points. ii. Sketch the bifurcation diagram, and indicate the behaviour of non- equilibrium solutions using appropriate arrows. ii. Find all bifurcation points and classify them. 10 Marks (b) Consider the second order differential equation i. Show that (1) can be written as the system of ordinary differential equations (y R for...
For each problem, sketch all of the qualitatively different vector fields that occur as the parameter u is varied. Find the values of u at which bifurcation occur, and classify the bifurcations. Finally, sketch the bifurcation diagram or the steady states x* vs the parameter u. 1. ** = 5 – ļe-x? 2. espe= ux - T H > 0.
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