1. Graph the phase portrait of the system 12 3. - Ai where A A =
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- Graph the phase portrait of the system..The longitude, rt of an air plane is affected by a random component e, due to the wind effect and its speed t It = -1 + 20t-1 + 6t. The speed of the plane is affected by a constant global linear trend, ß = B₁-1 = 3, and varies randomly due to weather conditions, v₁ = V₁-1 + B₁-1+w₂. In the above equations, is assumed to be white Gaussian noise with zero mean and o = 3. Similarly w is assumed to be white Gaussian noise with zero mean and 2,=0.5. A GPS transmitter mounted on the plane sends a noisy measurement to a receiver about its position, X₁ = 0.5xt + nt, where n, is assumed to be white Gaussian noise with zero mean and o2 = 2. (a) Using the following definition for the state vector, 0t. 0₁ It + ve B₂ write the motion of the plane in state space form. Note: You need to provide the exact form of the h, G and W matrices. (b) Evaluate the initial estimate for the state vector 03-Help with parts a through e, having some difficulty with the phase lines.
- plot phase portrait of the following Nonlinear system. x₁ = 29₂2₂ - XG X₂₂ 1x²2₂² = -296²³-96₂Match each linear system with one of the phase plane direction fields. (The blue lines are the arrow shafts, and the black dots are the arrow tips.) ? ✓ | 1. z ' = || a' ? 2. ': = ? 3.' = 4. a: = 11 8] -10 3 1 5 -2 1 -5 -13 10] -10 x2 A x2 с x1 (x2 B 2x2/ D Note: To solve this problem, you only need to compute eigenvalues. In fact, it is enough to just compute whether the eigenvalues are real or complex and positive or negative.Match each linear system with one of the phase plane direction fields. (The blue lines are the arrow shafts, and the black dots are the arrow tips.) -5 2 v 1. a' = 1 5 3 ? v 2. a' = 1 -7 12 3. z' = 9 -8 ? v 4. a' -9 C D.
- Draw the phase portraits of the following linear systems and justify the choice of the direction of trajectories. (4.1) * = ( 13 1³ ) *. X, -3 (4.2) = *-(34)x X.The systems are given uh need to draw the phase portrait for these 3 sysytemsA new town was incorporated in 1960. The size of the town's population was recorded every 5 years after 1960. Using the variables x, for number of years since 1960, and y, for the size of the population, three models were created to predict the population from the number of years since 1960.
- Show that following system is reversible, and sketch the phase portrait.= Find the general solution of the given system. Use a computer system or graphing calculator to construct a direction field and typical solution curves for the system. x' = -4 1 -6 Xx' = 1 х. Construct the phase plane for the points (2,2), (2,0), (2,-2), (0,2), (0,-2), (-2,2), (-2,0) and (-2,-2). 2.5 1.5 1 0.5 -0.5 -1 -1.5 -2 -2.5 3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2.5