It can be shown that D = (u, v): u >= 1/16, 0 <= v <=128, u + v <=130 is a differenti...
It can be shown that D = (u, v): u >= 1/16, 0 <= v <=128, u + v <=130 is a differential based on a trimolecular reaction model. u' = 1/8 - u + v^2v and v' = 1/2 -u^2v. Use the Poincare-Bendixion Theorem to determine if the system has a periodic solution.
Homework Answers
I do know of the positive Poincaré-Bendixson test: Let R be an invariant region for a plane autonomous system and suppose that R has no critical point on the boundary. Then
- If R is a simply connected region that has a single unstable node or unstable spiral point in it's interior, then there's at least one periodic solution in R.
- If R is an annular region that contains no critical point of the system, then there is at least one periodic solution in R.
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It can be shown that D = (u, v): u >= 1/16, 0 <= v <=128, u + v <=130 is a differenti...
ysing laplace transform 25.15. u"-2v = 2 u+v 5e2+ 1; JCOU u(0)2, u(0) 2, v(0) = 1 25.15. u"-2v = 2 u+v 5...
ysing laplace transform
25.15. u"-2v = 2 u+v 5e2+ 1; JCOU u(0)2, u(0) 2, v(0) = 1
25.15. u"-2v = 2 u+v 5e2+ 1; JCOU u(0)2, u(0) 2, v(0) = 1
help, pls tq. 4. Consider the first order autonomous system d13-1 0)-1. (a) Estimate the solution of the system (1) at t0.2 using two steps of Euler's method with 2v, u(0)0 step-size h 0.1 T1+C2+...
help, pls tq.
4. Consider the first order autonomous system d13-1 0)-1. (a) Estimate the solution of the system (1) at t0.2 using two steps of Euler's method with 2v, u(0)0 step-size h 0.1 T1+C2+A1-4 (b) An autonomous system of two first order differential equations can be written as: du dt=f(mu), u(to) = uo, dv dt=g(u, u), u(to) to. The Improved Euler's scheme for the system of two first order equations is tn+1 = tn + h, Use the Improved...
Help would be greatly appreciated!! 1. Let S be the surface in R3 parametrized by the vector function ru, v)(,-v, v+ 2u) with domain D-{(u, u) : 0 u 1,0 u 2). This surface is a plane segment shaped...
Help would be greatly appreciated!!
1. Let S be the surface in R3 parametrized by the vector function ru, v)(,-v, v+ 2u) with domain D-{(u, u) : 0 u 1,0 u 2). This surface is a plane segment shaped like a parallelogram, and its boundary aS (with positive orientation) is made up of four line segments. Compute the line integral fos F -dr where F(z, y, z) = 〈エ2018 + y, 2r, r2-Ins). Hint: use Stokes' theorem to transform this...
Q6 - 21 Let u : | -71, v-| -31, and w=| 27 |. It can...
Q6
- 21 Let u : | -71, v-| -31, and w=| 27 |. It can be shown that-3u-2v-w=0. Use this fact (and no row 4 - 21 27 2 x1 operations) to find x1 and X2 that satisfy the equation73 4-7 2 2 (Simplify your answers.)
1. Let u be a solution of the wave equation u 0. Let the points A, B, C, D be the vertices of the...
1. Let u be a solution of the wave equation u 0. Let the points A, B, C, D be the vertices of the paralleogram formed by the two pairs of characteristic lines r-ctC1,x- ct-2,+ ct- di,r +ct- d2 Show that u (A)+u (C)-u (B) + u (D Use this to find u satisfying For which (x, t) can you determine u (x, t) uniquely this way? 2. Suppose u satisfies the wave equation utt -curr0 in the strip 0...
We can apply the Method of Separation of Variables to obtain a representation for the solution u ...
Please show all work and provide and an original solution.
We can apply the Method of Separation of Variables to obtain a representation for the solution u u(, t) for the following partial differential equation (PDE) on a bounded domain with homogeneous boundary conditions. The PDE model is given by: u(r, 0) 0, (2,0) = 4. u(0,t)0, t 0 t 0 (a) (20 points) Assume that the solution to this PDE model has the form u(x,t) -X (r) T(t). State...
5. Consider the nonlinear two dimensional Lotka-Volterra (predator-prey) system z'(t) = z(t)[2-2(...
5. Consider the nonlinear two dimensional Lotka-Volterra (predator-prey) system z'(t) = z(t)[2-2(t)-2y(t)l, y'(t) = y(t)12-y(t)--2(t)] (a) Find all critical points of this system, and at each determine whether or not the system is locally stable or unstable. (b) We proved in class, using the Bendixson-Dulac theorem, that this system has no periodic solution with trajectory in the first quadrant of the plane. Assuming this, use the Poincare-Bendixson theorem to prove that all trajectories (z(t),y(t)) of the system (2) with initial...
1. Consider the circuit shown below. Cl e, (0) c, e。(t) Find the transfer function below using t...
Please help with this dynamics circuit
analysis.
Please show work and explain.
Thank you!!
1. Consider the circuit shown below. Cl e, (0) c, e。(t) Find the transfer function below using time-domain and impedance methods. (a) Determine the differential equation for the relationship between eo(1) and e(1) (b) Find the transfer function E, (s)/E,(s) and determine the system time constant in terms of the circuit element values C, C, and R 17 2 (c) Find the transfer function E, (s)/E,...
JWV) - V ior U21 and U <1 < 0. (6) Losses have a Weibull distribution....
JWV) - V ior U21 and U <1 < 0. (6) Losses have a Weibull distribution. A random sample of 16 losses is 54, 70, 75, 81 84. 88, 97, 105, 109, 114, 122, 125, 128, 139, 146, and 153. Use percentile matching! with the 20th and 70th percentiles to estimate the parameters 7 and 8.
6-7. Given vectors U = -41 +12). V = 5i - 21,W=-31 - 1 6. Find...
6-7. Given vectors U = -41 +12). V = 5i - 21,W=-31 - 1 6. Find a) 30 - 5.b) |2V - WI 7. a) U. W What can you tell from the result? b) angle between U and keep one digit after decimal, calculator ok) 8. a) Write the complex number -2 -21 in trigonometry form. Be sure to graph when looking for O. (No decimal answer) b) use the result from a) and De Moivre's theorem the find...
ysing laplace transform
25.15. u"-2v = 2 u+v 5e2+ 1; JCOU u(0)2, u(0) 2, v(0) = 1
25.15. u"-2v = 2 u+v 5e2+ 1; JCOU u(0)2, u(0) 2, v(0) = 1
help, pls tq.
4. Consider the first order autonomous system d13-1 0)-1. (a) Estimate the solution of the system (1) at t0.2 using two steps of Euler's method with 2v, u(0)0 step-size h 0.1 T1+C2+A1-4 (b) An autonomous system of two first order differential equations can be written as: du dt=f(mu), u(to) = uo, dv dt=g(u, u), u(to) to. The Improved Euler's scheme for the system of two first order equations is tn+1 = tn + h, Use the Improved...
Help would be greatly appreciated!!
1. Let S be the surface in R3 parametrized by the vector function ru, v)(,-v, v+ 2u) with domain D-{(u, u) : 0 u 1,0 u 2). This surface is a plane segment shaped like a parallelogram, and its boundary aS (with positive orientation) is made up of four line segments. Compute the line integral fos F -dr where F(z, y, z) = 〈エ2018 + y, 2r, r2-Ins). Hint: use Stokes' theorem to transform this...
Q6
- 21 Let u : | -71, v-| -31, and w=| 27 |. It can be shown that-3u-2v-w=0. Use this fact (and no row 4 - 21 27 2 x1 operations) to find x1 and X2 that satisfy the equation73 4-7 2 2 (Simplify your answers.)
1. Let u be a solution of the wave equation u 0. Let the points A, B, C, D be the vertices of the paralleogram formed by the two pairs of characteristic lines r-ctC1,x- ct-2,+ ct- di,r +ct- d2 Show that u (A)+u (C)-u (B) + u (D Use this to find u satisfying For which (x, t) can you determine u (x, t) uniquely this way? 2. Suppose u satisfies the wave equation utt -curr0 in the strip 0...
Please show all work and provide and an original solution.
We can apply the Method of Separation of Variables to obtain a representation for the solution u u(, t) for the following partial differential equation (PDE) on a bounded domain with homogeneous boundary conditions. The PDE model is given by: u(r, 0) 0, (2,0) = 4. u(0,t)0, t 0 t 0 (a) (20 points) Assume that the solution to this PDE model has the form u(x,t) -X (r) T(t). State...
5. Consider the nonlinear two dimensional Lotka-Volterra (predator-prey) system z'(t) = z(t)[2-2(t)-2y(t)l, y'(t) = y(t)12-y(t)--2(t)] (a) Find all critical points of this system, and at each determine whether or not the system is locally stable or unstable. (b) We proved in class, using the Bendixson-Dulac theorem, that this system has no periodic solution with trajectory in the first quadrant of the plane. Assuming this, use the Poincare-Bendixson theorem to prove that all trajectories (z(t),y(t)) of the system (2) with initial...
Please help with this dynamics circuit
analysis.
Please show work and explain.
Thank you!!
1. Consider the circuit shown below. Cl e, (0) c, e。(t) Find the transfer function below using time-domain and impedance methods. (a) Determine the differential equation for the relationship between eo(1) and e(1) (b) Find the transfer function E, (s)/E,(s) and determine the system time constant in terms of the circuit element values C, C, and R 17 2 (c) Find the transfer function E, (s)/E,...
JWV) - V ior U21 and U <1 < 0. (6) Losses have a Weibull distribution. A random sample of 16 losses is 54, 70, 75, 81 84. 88, 97, 105, 109, 114, 122, 125, 128, 139, 146, and 153. Use percentile matching! with the 20th and 70th percentiles to estimate the parameters 7 and 8.
6-7. Given vectors U = -41 +12). V = 5i - 21,W=-31 - 1 6. Find a) 30 - 5.b) |2V - WI 7. a) U. W What can you tell from the result? b) angle between U and keep one digit after decimal, calculator ok) 8. a) Write the complex number -2 -21 in trigonometry form. Be sure to graph when looking for O. (No decimal answer) b) use the result from a) and De Moivre's theorem the find...
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