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(3) - F(2,4) to Consider a system of differential equations describing the progress of a disease...
Assignment 8 Remaining Time: 131:53:22 Question 1 Consider a system of differential equations describing the progress of a disease in a population, given by F(x, y) for 1 point How Did I Do? a vector-valued function F. In our particular case, this is: d' = 3 – 3xy - 12 y' = 3xy – 34 where x(t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of...
Consider a system of differential equations describing the progress of a disease in a population, given byF, ) for a vector-valued function F. In our particular case, this IS. where z(t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of individuals is counted in units of 1,000 individuals a) Find the nullclines (simplest form) of this system of differential equations. The x-nullcline is y 2/3 The...
just (A) (B) (C) 3. Consider the system of differential equations = z+9-1 (a) Sketch the r-nullcline, where solutions must travel vertically. Identify the regions (b) On a separate set of axes, sketch the y-nullcline, where solutions must travel horizon in the plane where solutions will move toward the right, and where solutions move toward the right tally. Identify the regions in the plane where solutions will move upward, and where solutions move downward. (c) On a third set of...
Consider the system of linear differential equations z,(t)-17/11 z(t) + 9/11 y(t) y,(t)-18/11 z(t) + 38/11 y(t) a) Find the equation of the x-nullcline. Write your answer as an equation in z and y Answer b) Find the equation of the y-nullcline. Write your answer as an equation of z and y Answer. c) The nullclines divide the plane into four regions as illustrated below. 忽聡 2 -2 2 -2 For each of the regions, determine the direction of the...
Consider the system of equations dxdt=x(3−x−4y) dydt=y(1−3x), taking (x,y)>0. (1 point) Consider the system of equations de = 2(3 – 2 – 49) = y(1 - 33), taking (2,y) > 0. (a) Write an equation for the (non-zero) vertical (-)nullcline of this system: (Enter your equation, e.g., y=x.) And for the (non-zero) horizontal (y-)nullcline: (Enter your equation, e.g. y=x.) (Note that there are also nullclines lying along the axes.) (b) What are the equilibrium points for the system? Equilibria =...
2. (28 marks) This questions is about the following system of equations x = (2-x)(y-1) (a) Find all equilibrium solutions and determine their type (e.g., spiral source, saddle) Hint: you should find three equilibria. b) For each of the equilibria you found in part (a), draw a phase portrait showing the behaviour of solutions near that equilibrium. -2 (c) Find the nullclines for the system and sketch them on the answer sheet provided. Show the direction of the vector field...
Consider a system described by the following equations: · 1 = I1 – 2x122 + u, º2 = X122 – 22, where x = (x1, x2) is the state and u is an input. (a) Find all equilibrium points for u = 0. (b) For each equilibrium point x = (ū1, 72), find the linearization of the system about the equilibrium. Express your results in state- space form, ż= Az + Bu, where z=x-. Also give the output equation y=...
Consider the system of two coupled differential equations: y-cx + dy, x-ax + by, with the equilibrium solution (xe,ye) = (0,0) (a) Rewrite the coupled system as a matrix differential equation and identify the matrix A. Obtain a general solution to the matrix differential equation in terms of eigenvectors and eigenvalues of A. Justify your answer (b) Classify possible types and stability of the equilibrium with dependence on the eigenvalues of A. (Note: You are not asked to compute the...
(1 point) Consider the system of differential equations -28y1 + 14y22 -35y1 + 14y2 a. Rewrite this system as a matrix equation ý' = Aj. j' = [ ] ý b. Compute the eigenvalues of the coefficient matrix A and enter them as a comma separated list.
Differential Equations for Engineers II Page 1 of 6 1. The interface y(x) between air and water in a time-independent open channel flow can be approximated with the second order ODE day d2 +oʻy=0, 20, (1) 1 mark 2 marks 5 marks where the parameter a? is a measure of the mean speed of the flow. The flow is in the positive x direction (i.e. from left to right). (a) Re-write equation (1) as a system of first-order ODEs by...