Identifying cusp catastrophes?

[Set Abominae]

Hi everyone.

I have a system with two strictly positive parameters, for which we have a single equilibrium point or 3 equilibrium points if a certain inequality holds involving the two parameters.

I'm struggling to identify whether or not this is an example of a cusp catastrophe or not.

I know I'm supposed to be looking at the following equations:

V(x)=(x^4)/4 + (ax^2)/2 + bx

and

4(a^3) + 27(b^2) = 0

,but I'm generally unsure as to how to proceed.

Any nudges in the right direction would be helpful (I'm not listing the equations because I'm only looking for help with the theory...)

Thanks in advance, everyone :)

 

[fresh_42]

I have a system with two strictly positive parameters, for which we have a single equilibrium point or 3 equilibrium points if a certain inequality holds involving the two parameters.

To receive a meaningful answer, you will have to explain your explanation first. It is not clear how your equilibriums are defined.