The Continuous Time Model of Computation defines a semantics used for continuous-time simulations. Continuous Time models consist of Actors that have continuous time signals as their inputs and outputs, and may have a state that changes over time advancement. These actors are connected by relations denoting particular signals. At a sequence of time increments, the values of all signals are determined using a continuous time solving algorithm. If a given precision cannot be accomplished, finer time increments are used adaptively.

The domain models systems with continuous dynamics, including for example analog circuits and mechanical systems, but also cleanly supports discrete events, modal behaviors, and signals that mix continuous-time behaviors with discrete events. Models for continuous dynamics are equivalent to linear or nonlinear integral equations. A sophisticated numerical solver for these equations is integrated with the director. The clean semantics of the Continuous domain enables its integration in hierarchical heterogeneous models that use the Synchronous/Reactive (SR) and Discrete Event (DE) domains. Arbitrary hierarchical mixtures of these domains are supported, although if SR is at the top level, then the period parameter of the director must be used so that time advances. Domain interactions are documented in Lee and Zheng, 2007.

The clean semantics of the Continuous domain enables its integration
in hierarchical heterogeneous models that use the Synchronous/Reactive (SR)
and Discrete Event (DE) domains. Arbitrary hierarchical mixtures of these
domains are supported, although if SR is at the top level, then the
*period* parameter of the director must be used so that time advances.
Domain interactions are documented in Goderis et al.

- Janette Cardoso, Edward A. Lee, Jie Liu and Haiyang Zheng, "Continuous-Time Models,"
a chapter from

Claudius Ptolemaeus, Editor, "System Design, Modeling, and Simulation Using Ptolemy II", Ptolemy.org, 2014. (included in the release as`$PTII/doc/books/systems/PtolemyII_DigitalV1_02.pdf`

)

The models provided in this chapter are also available online.
In System Design, Modeling, and Simulation using Ptolemy II. Ptolemy.org 2014.
- A. Goderis, C. Brooks, I. Altintas, E. A. Lee, and C. Goble, "Heterogeneous Composition of Models of Computation," EECS Department, University of California, Berkeley, Tech. Rep. UCB/EECS-2007-139, Nov. 2007.
- Edward A. Lee, Haiyang Zheng, "Leveraging Synchronous Language Principles for Heterogeneous Modeling and Design of Embedded Systems," EMSOFT, September 30 - October 2, 2007, Salzburg, Austria.
- Haiyang Zheng, "Operational Semantics of Hybrid Systems," Ph.D. Dissertation, EECS Department, University of California, Berkeley, Technical Report No. UCB/EECS-2007-68, May 18, 2007.
- Edward A. Lee and Haiyang Zheng, "Operational Semantics of Hybrid Systems," Invited paper in
*Proceedings of Hybrid Systems: Computation and Control*(HSCC) LNCS 3414, Zurich, Switzerland, March 9-11, 2005, pp.25-53.