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In Exercises 1-6, locate the bifurcation values for the one-parameter family and draw the phase lines...
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)
4. Locate the bifurcation values for the one parameter family: y = y2 - 2y +...
4. Locate the bifurcation values for the one parameter family: y = y2 - 2y + 1. Draw the phase lines for the values of the parameter smaller, larger, and equal to each bifurcation value.
sketch phase lines for: dy/dt = y(y+3)^3(y-2)^2(y-5) sketch bifurcation diagram for: dy/dt = y(y^2+ α) where...
sketch phase lines for: dy/dt = y(y+3)^3(y-2)^2(y-5) sketch bifurcation diagram for: dy/dt = y(y^2+ α) where α is a parameter
(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...
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
Consider the family of differential equations dy/dx=y^3+ky+k^2 Are there any equilibrium solutions when k=0? Draw bifurcation...
Consider the family of differential equations dy/dx=y^3+ky+k^2 Are there any equilibrium solutions when k=0? Draw bifurcation diagram Draw phase diagram for when k=1/2 Does limit exist when k=1/2 and y(0)=0
Problems 17 through 19 deal with competitive systems much like those in Examples 1 and 2 except t...
#19 all parts
Problems 17 through 19 deal with competitive systems much like those in Examples 1 and 2 except that some coefficients depend on a parameter a. In each of these problems, assume that x, y, and a are always nonnegative. In each of Problems 17 through 19: (a) Sketch the nullclines in the first quadrant, as in Figure 9.4.5. For different ranges of a your sketch may resemble different parts of Figure 9.4.5 (b) Find the critical points...
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...
Pls choose the answer like a,b,c,d for these 5 multichoice question don't mind what i choose
pls choose the answer like a,b,c,d for these 5 multichoice
question don't mind what i choose
What can be said about the following differential equation? dy 7t It is autonomous, non-separable, linear and non-homogenous It is non-autonomous, non-separable, linear and non-homogenous It is autonomous, separable, linear and homogenous It is autonomous, separable, linear and non-homogenous. Consider the following differential equation: dt the function FA(x) -22 A, with A0, undergoes a bifurcation. Identify the type of bifurca tion. F has two...
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...
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)
4. Locate the bifurcation values for the one parameter family: y = y2 - 2y + 1. Draw the phase lines for the values of the parameter smaller, larger, and equal to each bifurcation value.
(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...
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
Consider the family of differential equations dy/dx=y^3+ky+k^2 Are there any equilibrium solutions when k=0? Draw bifurcation diagram Draw phase diagram for when k=1/2 Does limit exist when k=1/2 and y(0)=0
#19 all parts
Problems 17 through 19 deal with competitive systems much like those in Examples 1 and 2 except that some coefficients depend on a parameter a. In each of these problems, assume that x, y, and a are always nonnegative. In each of Problems 17 through 19: (a) Sketch the nullclines in the first quadrant, as in Figure 9.4.5. For different ranges of a your sketch may resemble different parts of Figure 9.4.5 (b) Find the critical points...
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...
pls choose the answer like a,b,c,d for these 5 multichoice
question don't mind what i choose
What can be said about the following differential equation? dy 7t It is autonomous, non-separable, linear and non-homogenous It is non-autonomous, non-separable, linear and non-homogenous It is autonomous, separable, linear and homogenous It is autonomous, separable, linear and non-homogenous. Consider the following differential equation: dt the function FA(x) -22 A, with A0, undergoes a bifurcation. Identify the type of bifurca tion. F has two...
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...
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