Consider a system of differential equations describing the progress of a disease in a population,...
(3) - F(2,4) to Consider a system of differential equations describing the progress of a disease in a population, given by for a vector-valued function F. In our particular case, this is: t' = 3 – 3zy - 12 y' – 3ay – 2y where I (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. and =...
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 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...
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...
2 This system has an equilibrium point at the origin (you do not have to show this) For parts (d)-(e), consider the system This system also has an equilibrium point at the origin (you do not have to show this). (d) (4 pts) Compute the linearization of this system, and conclude that the Jacobian yields no relevant infor- mation regarding the equilibrium at (0,0). (e) (3 pts) Sketch the nullcline diagram for this system. Conclude from the diagram that the...
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 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 =...
Consider the non-linear system y-y(1-x-y). (a) Find equations for all of the x- and y-nullclines. (b) Find the coordinates of each equilibrium point of the system. (c) Sketch the nullclines in the phase plane. Clearly mark the equilibrium points. Also indicate the direction of flow on the nullclines. Consider the non-linear system y-y(1-x-y). (a) Find equations for all of the x- and y-nullclines. (b) Find the coordinates of each equilibrium point of the system. (c) Sketch the nullclines in the...
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=...
(1 point) Consider the system of higher order differential equations 2 Rewrite the given system of two second order differential equations as a system of four first order linear differential equations of the formy - P(t)y + g(t). Use the following change of variables y (t) y2(t)y'(t) 3 (t) y(t) у(t) z(t) -y2 4 (1 point) Consider the system of higher order differential equations 2 Rewrite the given system of two second order differential equations as a system of four...