In 1722, use the graphical approach for 2 2 systems to find the sign structure of the

Chapter 11, Problem 21

(choose chapter or problem)

In 1722, use the graphical approach for 2 2 systems to find the sign structure of the Jacobi matrix at the indicated equilibrium. If possible, determine the stability of the equilibrium. Assume that the system of differential equations is given by dx1 dt = f1(x1, x2) dx2 dt = f2(x1, x2) Furthermore, assume that x1 and x2 are both nonnegative. In each problem, the zero isoclines are drawn and the equilibrium we want to investigate is indicated by a dot. Assume that both x1 and x2 increase close to the origin and that f1 and f2 change sign when crossing their zero isoclines. See Figure 11.47. x2 x1 _ 0 dx2 dt _ 0 dx1 dt Figure 11.47