Re: cusp fold surface

*To*: mathgroup at smc.vnet.net*Subject*: [mg69825] Re: cusp fold surface*From*: "Narasimham" <mathma18 at hotmail.com>*Date*: Sat, 23 Sep 2006 23:45:36 -0400 (EDT)*References*: <ef2tul$msr$1@smc.vnet.net>

dwarnold45 at cox.net wrote: > All, > > Has anyone done a bifurcation analysis of dx/dt=h+rx-x^3, where h and r > are parameters? > > I am looking for some mathematica code that will darw cusp catastrophe > surface above bifurcation curves in the (r,h) plane. > > Thanks. Hint: Let t = s so that we have unit tangent velocity along the curve. Slope of curve is phi, dx/ds = cos(ph) , dy/ds = sin(ph). The roots of RHS are the turning points at cusp.