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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.