ABSTRACT
Consider the blow-up ODE problem (454), which is a difficult one, with a 5D phase space. Note that, by invariant scaling (407), it can be reduced to a 4th-order ODE with an even more complicated nonlinear operator composed of too many polynomial terms, so we do not rely on that and work in the original phase space. Therefore, some more delicate issues on, say, uniqueness of certain orbits, become very difficult or even remain open, though some more robust properties can be detected rigorously. We will also use numerical methods for illustrating and justifying some of our conclusions. As before, for the fifth-order equations such as (454), this and further numerical constructions are performed in MATLAB with the standard ode45 solver.
