Event-Driven System:
An event-driven system is dynamical or a discrete system, where the evolution of the system is guided by the events.
In event-driven systems, the state changes only upon the (typically) asynchronous occurrence of events.
For these system time is a dependent variable (it depends on the events)
So the state of an event-driven system is NON-DIFFERENTIABLE, so the system cannot be modeled by differential equations.
Example of Event-Driven System: Queuing System

- Here the events are: arrivals, and departures
- The system graph cannot have a continuous function, arrival do not change gradually, the same for departures, so it will result in something like:
