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 origin is a sink (Hint: The nullclines of this system divide the plane into 6 regions. Start in any of these regions off of a ullelie. Wlhre do yo go? Is this rne for evry reion?)
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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...
Assignment 8 Remaining Time: 131:53:22 Question 1 Consider a system of differential equations describing the progress...
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...
4. Consider the system ry(1 +) -(42 2) (a) Show that the origin is an equilibrium point and it is...
4. Consider the system ry(1 +) -(42 2) (a) Show that the origin is an equilibrium point and it is a source (b) (For practice only, not to be handed in). Show that the system has no other equilibrium points (c) Find a value of C such that the set is positively invariant respect to the flow of (2) (d) Show that (2) has a periodic orbit in S.
4. Consider the system ry(1 +) -(42 2) (a) Show that...
dx/dt = 4x -x^2 -2xy dy/dt = -y+0.5 xy a) find equilibrium points b) find Jacobian matrix for above system c) find Jacobian matrix at eq. point (0,0) d) draw phase portrait near (0,0) from © e) show...
dx/dt = 4x -x^2 -2xy dy/dt = -y+0.5 xy a) find equilibrium points b) find Jacobian matrix for above system c) find Jacobian matrix at eq. point (0,0) d) draw phase portrait near (0,0) from © e) show at eq. point (4,0) the Jacobian matrix is -4 -8 0 1 f) draw phase portrait near (4,0) from (d) g) at eq. point (2,1) the Jacobian matrix is -2 -4 0.5 0 h) draw phase portrait near (2,1) from (f) i)...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
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...
4. Consider the system ry(1 +) -(42 2) (a) Show that the origin is an equilibrium point and it is a source (b) (For practice only, not to be handed in). Show that the system has no other equilibrium points (c) Find a value of C such that the set is positively invariant respect to the flow of (2) (d) Show that (2) has a periodic orbit in S.
4. Consider the system ry(1 +) -(42 2) (a) Show that...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
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