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(1 point) Use the applet provided to draw a phase portrait for ' = -2x(1 -...
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
1. Draw the orbit analysis or phase portrait of f(x) = x3 - X. 2. Find...
1. Draw the orbit analysis or phase portrait of f(x) = x3 - X. 2. Find the neutral fixed point of g(x) = x - *3. Use graphical analysis to determine if the fixed point is weakly attracting, weakly repelling, or neither.
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...
4. Autonnomous equations: Sec 1.6: Autonomous equations Determine which differential equation corresponds to each phase diagram....
4.
Autonnomous equations:
Sec 1.6: Autonomous equations Determine which differential equation corresponds to each phase diagram. You should be able to state briefly how you know your choices are correct. ? . 1. = gi? 32 2. = ? |: - 21 ? 3. = (- 2) ? • 4. * - 42 ? 5. = 21 - 22 42- A B C E F G H
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...
x'=r (1 - 2 / 2 x where r and K are positive constants, is called...
x'=r (1 - 2 / 2 x where r and K are positive constants, is called the logistic equation. It is used in a number of scientific disciplines, but primarily (and historically) in population dynamics where z(t) is the size (numbers or density) of individuals in a biological population. For application to population dynamics ä(t) cannot be negative. If the solution (t) vanishes at some time, then we interpret this biologically as population extinction. (a) Draw the phase line portrait...
1. The Duffing equation is a non-linear second-order differential equation used to model certain damped and...
1. The Duffing equation is a non-linear second-order differential equation used to model certain damped and driven oscillators. The equation is given by -ax+3x3 = cos(wt) at medt dr. where function r = r(t) is the displacement at timet, is the velocity, and is the acceleration. The parameter 8 controls the amount of damping, a controls the linear stiffness, B controls the amount of non-linearity in the restoring force, and 7 and w are the amplitude and angular frequency of...
please show all steps 1.) 2.) 3. (a) In each of (1) and (2), determine whether...
please show all steps
1.)
2.)
3.
(a) In each of (1) and (2), determine whether the given equation is linear, separable, Bernoulli, homogeneous, or none of these. (1) y = yenye (2) x²y = 3x cos(2x) + 3xy (b) Find the general solution of (1). Given the one-parameter family y3 = 3 +Cx? (a) Find the differential equation for the family. (b) Find the differential equation for the family of orthogonal trajectories. (e) Find the family of orthogonal trajectories....
(1 point) Calculate the eigenvalues of this matrix: [Note-- you'll probably want to use a calculator...
(1 point) Calculate the eigenvalues of this matrix: [Note-- you'll probably want to use a calculator or computer to estimate the roots of the polynomial which defines the eigenvalues. You also may want to view a phase plane plot (right click to open in a new window).]] 46 A -4 38 -5 smaller eigenvalue associated eigenvector = larger eigenvalue associated, eigenvector (1 point) Consider the system of differential equations dr dt 3x + 0.5y, dy 2.5x + y. dt 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
1. Draw the orbit analysis or phase portrait of f(x) = x3 - X. 2. Find the neutral fixed point of g(x) = x - *3. Use graphical analysis to determine if the fixed point is weakly attracting, weakly repelling, or neither.
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...
4.
Autonnomous equations:
Sec 1.6: Autonomous equations Determine which differential equation corresponds to each phase diagram. You should be able to state briefly how you know your choices are correct. ? . 1. = gi? 32 2. = ? |: - 21 ? 3. = (- 2) ? • 4. * - 42 ? 5. = 21 - 22 42- A B C E F G H
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...
x'=r (1 - 2 / 2 x where r and K are positive constants, is called the logistic equation. It is used in a number of scientific disciplines, but primarily (and historically) in population dynamics where z(t) is the size (numbers or density) of individuals in a biological population. For application to population dynamics ä(t) cannot be negative. If the solution (t) vanishes at some time, then we interpret this biologically as population extinction. (a) Draw the phase line portrait...
1. The Duffing equation is a non-linear second-order differential equation used to model certain damped and driven oscillators. The equation is given by -ax+3x3 = cos(wt) at medt dr. where function r = r(t) is the displacement at timet, is the velocity, and is the acceleration. The parameter 8 controls the amount of damping, a controls the linear stiffness, B controls the amount of non-linearity in the restoring force, and 7 and w are the amplitude and angular frequency of...
please show all steps
1.)
2.)
3.
(a) In each of (1) and (2), determine whether the given equation is linear, separable, Bernoulli, homogeneous, or none of these. (1) y = yenye (2) x²y = 3x cos(2x) + 3xy (b) Find the general solution of (1). Given the one-parameter family y3 = 3 +Cx? (a) Find the differential equation for the family. (b) Find the differential equation for the family of orthogonal trajectories. (e) Find the family of orthogonal trajectories....
(1 point) Calculate the eigenvalues of this matrix: [Note-- you'll probably want to use a calculator or computer to estimate the roots of the polynomial which defines the eigenvalues. You also may want to view a phase plane plot (right click to open in a new window).]] 46 A -4 38 -5 smaller eigenvalue associated eigenvector = larger eigenvalue associated, eigenvector (1 point) Consider the system of differential equations dr dt 3x + 0.5y, dy 2.5x + y. dt For...
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