Orbital and equilibrium dynamics of a multiwell potential

We consider a Hamiltonian system associated with the two-well umbilical catastrophe potential , while the corresponding potential contains only one free parameter. We determine how this free parameter affects the equilibrium dynamics of the system by computing their coordinates on the configuration plane, along with their linear stability and type. Additionally, we discuss the influence of the same free parameter on the orbital dynamics of the system by performing a systematic and thorough orbit classification that allows us to reveal the bounded or escaping motion of the test particle.