# Continuous Time

The Continuous Time (CT) Domain aims to help the design of systems that have continuous dynamic, for example, analog circuits, mechanical systems, and the continuous environment for embedded systems. Models in the CT domain has the form of ordinary differential equations (ODEs):

``````        dx/dt = f(x, u, t)
y = g (x, u, t)```
```
where `x` is the state of the system, `u` is the input, and `y` is the output. Time `t`in the model is continuous, and `dx/dt` is the derivative of `x` with respective to time.

The simulation of a continuous-time system is to solve (numerically) the ODEs of the system. There is a variety of ODE solving methods developed in decades. A class of them, called the time marching methods, discretizes time into discrete points and finds the value of `x` at these points at an increasing order of time. Ptolemy II implements some of the time marching methods, like the forward Euler method, the backward Euler method, the 2(3) order Runge-Kutta method, and the trapezoidal rule method.

The CT domain in Ptolemy II supports the interaction with event-based domains, like the discrete event (DE) domain and the finite state machine (FSM) domain, which yields the mixed-signal modeling and the hybrid system modeling. Event detectors are built in the CT domain library, so that the CT domain can always provide event-based interface to other domains when needed.

The CT domain supports mixed-signal modeling by a signal type system. To learn more about how to set signal types and how the type resolutions are done, please refer to the signal types page.

The `ct` domain is for use with the `fsm` domain.

The `continuous` domain is for use with the `modal` domain.

The CT domain is no longer being developed, please use the Continuous domain instead.