What does mean cusp and fold catastrophe in ELF analysis ?

mekelleche

Hello,
During my reading of some articles concerning the ELF analysis, I encountered some difficulties to understand the The combination of ELF analysis with Thom's catastrophe theory (CT), and some related expressions like cusp catastroph and fold catastroph.
What is the meaning of those expressions (I found for example : basin corresponds to Cusp catastrophe) ? and how this is related to bonding analysis ?
I need your help, it's very important.