Economics Dynamics Problems 169

Economics Dynamics Problems 169 - Systems of rst-order...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Systems of first-order differential equations 153 Figure 4.8. No matter what the initial point, it will be found that each trajectory approaches the fixed point ( x , y ) = (0 , 0). In other words, the fixed point (the equilibrium point) is globally stable. Considering the vector of forces for this system captures this feature. The equilibrium solution lines are y = 3 x for ˙ x = 0 y = x 3 for ˙ y = 0 with a fixed point at the origin. To the right of the x -line we have y < 3 x or 3 x + y < 0 implying ˙ x < 0 so x is falling While to the left of the x -line we have y > 3 x or 3 x + y > 0 implying ˙ x > 0 so x is rising Similarly, to the right of the y -line we have y < x 3 or 0 < 3 y + x implying ˙ y > 0 so y is rising While to the left of the y -line we have y > x 3 or 0 > 3 y + x implying ˙ y < 0 so y is falling All this information, including the vectors of force implied by the above results,
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern