I am trying to read some text books about hybrid dynamical system, in which maximal solution, bounded solution, and complete solution are mentioned frequently.
The following passage is a description about the solutions of hybrid dynamical system from the article I am reading. I cannot understand it well.
"The solution x to a hybrid system is nontrivial if dom x contains at least one point different from (0,0) ; maximal if it cannot be extended, that is, the hybrid system has no solution x' whose domain dom x' contains dom x as a proper subset and such that x' agrees with x on dom x; and complete if dom x is unbounded. Every complete solution is maximal."
How to understand "maximal ", bounded", and "complete" for solutions of a (hybrid) dynamical system? I hope the answers can be precise and easy to understand for a non-mathematics student.