‡ Download Dynamic Solver zipped which contains the wanted systems , Yours is Ms-system.ds: x'=y, y'=x-r*y-x*z, z'=-bz+x*x

Find (1) equilibrium states in the system, determine their type and find the stability boundaries in the (b,r) plane of
parameters, see Pages 911-912 of Appendix

(b) Find the eigenvalues and eigenvectors of the equilibrium state at the origin.

(c) Study two parameter cuts: b=1 and b=0.4. By decreasing the value of the parameter r (starting with 2), examine
the evaluation of the separatrices of the saddle. Find the critical values corresponding to the homoclinic bifurcations.
What is the saddle-index n there? Determine the stability of the bifurcating periodic orbits. Where does the symmetric
8-like periodic orbit come from? Consider the map x_{n+1}=(-\mu+Ax_{n}^{\nu})*sign(x), page 912 of Appendix

(d) On the path r=0.5 find the critical value corresponding to the appearance of the Lorenz attractror in the system, see
page 913 of Appendix

(e) Get your A and :-) Have a great summer!