Assistance needed for a, b, c.

b) What is the J acobian for this system at x=y=0? If b>0 and r 1. One solution is the negative of the other. Use the fact that x is a rotation rate, b > 0 and r > 1, to interpret them physically. To what physical conditions do the two solutions correspond? The differential equations that Lorentz derived are dx EGWX) d r = x xz dt y and dz = b. dt xy 2 The dependent variables are x(t), y(t) and z(t), whereas 6 and r are constant parameters. Physically, x(t) may be thought of as the rotation rate. The parameter 6 is a dimensionless iction coefficient, and r is a measure of the gravitational effect causing rotation relative to the friction and leakage that hinder rotation (stronger gravity or less friction increase r). You need not be concerned about the meaning of y(t) and z(t) (or the parameter b), you may think as them as quantities that are needed in order to obtain the rotation rate x(t). However, you may assume that b > 0. Use Matlab and/ or Mathematica (or the Wolam site) as needed to answer the questions below, but append copies of your work to your solution. a) Verify that x=y=z=0 is a xed point (or steady-state solution) for this system of three coupled ordinary differential equations