If matrices are stochastic (row stochastic) or doubly/bistochastic, we can make claims about the behavior of the discrete-time dynamical systems they represent. For example:
discrete-time Markov chains always converge to a steady-state distributions.
bistochastic systems converge to consensus states.
Does this intuition change when dealing with continuous-time linear systems? Or is there an analogous property that is required for continuous linear systems to converge in this way?