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4. Locate the bifurcation values for the one parameter family: y = y2 - 2y +...
dy 2. Locate the bifurcation values for the one-parameter family: = a- and draw the phase...
dy 2. Locate the bifurcation values for the one-parameter family: = a- and draw the phase lines for the parameter a slightly smaller than, slightly larger than, and at the bifurcation value. (15 points)
In Exercises 1-6, locate the bifurcation values for the one-parameter family and draw the phase lines...
In Exercises 1-6, locate the bifurcation values for the one-parameter family and draw the phase lines for values of the parameter slightly smaller than, slightly larger than, and at the bifurcation values. dy α-ly 6. dt
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...
Bifurcation dy Consider the autonomous differential equation =y? - 2y + 8. We will begin by...
Bifurcation dy Consider the autonomous differential equation =y? - 2y + 8. We will begin by examining dt the equilibrium solutions of the equation for various values of the parameter 8 1. Find the equilibrium solutions of the equation for 8 = -4,-2, 0, 2, 4 and make a sketch of the phase line for each value. Determine the stability of each equilibria. 2. Use a computer or some other means to sketch some solution curves for each value of...
4 1. Fix a value c, and then consider the one parameter family Find the value of λ (in terms of c) for which this family encounter a saddle-node bifurcation 4 1. Fix a value c, and then cons...
4 1. Fix a value c, and then consider the one parameter family Find the value of λ (in terms of c) for which this family encounter a saddle-node bifurcation
4 1. Fix a value c, and then consider the one parameter family Find the value of λ (in terms of c) for which this family encounter a saddle-node bifurcation
Problem 2: Consider the DE y = f(y) = y® – 2y + H, where is...
Problem 2: Consider the DE y = f(y) = y® – 2y + H, where is a real parameter. (i) Give the steady state(s) and determine their stability. There will be different cases, depending on . Draw the phase-line diagram for each case. What is the critical value of where the bifurcation happens? (ii) Draw a bifurcation diagram, indicating stable states with solid curves and unstable states with dashed curves.
(1 point) Use the applet provided to draw a phase portrait for ' = -2x(1 -...
(1 point) Use the applet provided to draw a phase portrait for ' = -2x(1 - 2)(2-2) The above equation could represent a model of a population that can become extinct if it drops below a particular critical value. What is this critical value? (1 point) Determine the bifurcation value(s) for the one parameter family k = 0 help (numbers) Determine which differential equation corresponds to each phase line. You should be able to state briefly how you know your...
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...
please answer the following questions. Please show all work and write your answers neatly and thoroughly...
please answer the following questions. Please show all work and
write your answers neatly and thoroughly please. Thank you.
2. Consider the one-parameter family of ordinary differential equations ay = y2 – 3y+a. Locate the bifurcation value of a and sketch the phase line for a value of a below, equal to, and above 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...
dy 2. Locate the bifurcation values for the one-parameter family: = a- and draw the phase lines for the parameter a slightly smaller than, slightly larger than, and at the bifurcation value. (15 points)
In Exercises 1-6, locate the bifurcation values for the one-parameter family and draw the phase lines for values of the parameter slightly smaller than, slightly larger than, and at the bifurcation values. dy α-ly 6. dt
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...
Bifurcation dy Consider the autonomous differential equation =y? - 2y + 8. We will begin by examining dt the equilibrium solutions of the equation for various values of the parameter 8 1. Find the equilibrium solutions of the equation for 8 = -4,-2, 0, 2, 4 and make a sketch of the phase line for each value. Determine the stability of each equilibria. 2. Use a computer or some other means to sketch some solution curves for each value of...
4 1. Fix a value c, and then consider the one parameter family Find the value of λ (in terms of c) for which this family encounter a saddle-node bifurcation
4 1. Fix a value c, and then consider the one parameter family Find the value of λ (in terms of c) for which this family encounter a saddle-node bifurcation
Problem 2: Consider the DE y = f(y) = y® – 2y + H, where is a real parameter. (i) Give the steady state(s) and determine their stability. There will be different cases, depending on . Draw the phase-line diagram for each case. What is the critical value of where the bifurcation happens? (ii) Draw a bifurcation diagram, indicating stable states with solid curves and unstable states with dashed curves.
(1 point) Use the applet provided to draw a phase portrait for ' = -2x(1 - 2)(2-2) The above equation could represent a model of a population that can become extinct if it drops below a particular critical value. What is this critical value? (1 point) Determine the bifurcation value(s) for the one parameter family k = 0 help (numbers) Determine which differential equation corresponds to each phase line. You should be able to state briefly how you know your...
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...
please answer the following questions. Please show all work and
write your answers neatly and thoroughly please. Thank you.
2. Consider the one-parameter family of ordinary differential equations ay = y2 – 3y+a. Locate the bifurcation value of a and sketch the phase line for a value of a below, equal to, and above 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...
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