Escape of two-DOF dynamical system from the potential well

We consider the escape of initially excited dynamical system with two degrees of freedom from a potential well. Three different benchmark well potentials with different topology are explored. The main challenge is to reveal the basic mechanisms that govern the escape in different regions of the parametric space and to construct appropriate asymptotic approximations for the analytic treatment of these mechanisms. In this study, numerical and analytical tools are used to classify and map the different escape mechanisms for a variety of initial conditions and to offer the analytic criteria predicting the system’s behavior for those cases.