# An algebra of open continuous time dynamical systems and networks

@article{Lerman2016AnAO, title={An algebra of open continuous time dynamical systems and networks}, author={Eugene Lerman and David I. Spivak}, journal={arXiv: Dynamical Systems}, year={2016} }

Many systems of interest in science and engineering are made up of interacting subsystems. These subsystems, in turn, could be made up of collections of smaller interacting subsystems and so on. In a series of papers David Spivak with collaborators formalized these kinds of structures (systems of systems) as algebras over presentable colored operads.
It is also very useful to consider maps between dynamical systems. This amounts to viewing dynamical systems as objects in an appropriate…

## 8 Citations

3 1 Ju l 2 02 0 OPEN SYSTEMS IN CLASSICAL MECHANICS

- Mathematics
- 2020

Span categories provide a framework for formalizing mathematical models of open systems in classical mechanics. The categories appearing in classical mechanics do not have pullbacks, which requires…

Open systems in classical mechanics

- Mathematics
- 2020

Author(s): Baez, John C; Weisbart, David; Yassine, Adam | Abstract: Span categories provide a framework for formalizing mathematical models of open systems in classical mechanics. The categories…

Lie 2-algebras of vector fields

- MathematicsPacific Journal of Mathematics
- 2020

We show that the category of vector fields on a geometric stack has the structure of a Lie 2-algebra. This proves a conjecture of R.~Hepworth. The construction uses a Lie groupoid that presents the…

Open Petri nets

- Computer ScienceMathematical Structures in Computer Science
- 2020

Two forms of semantics for open Petri nets are described using symmetric monoidal double functors out of pen(Petri), including an operational semantics and a reachability semantics that simply says which markings of the outputs can be reached from a given marking of the inputs.

Coarse-Graining Open Markov Processes

- Mathematics
- 2017

Coarse-graining is a standard method of extracting a simple Markov process from a more complicated one by identifying states. Here we extend coarse-graining to open Markov processes. An "open" Markov…

Agoric computation: trust and cyber-physical systems

- Computer Science
- 2018

This thesis reviews the logical and mathematical basis of stateless abstractions and takes steps towards the software implementation of agoric modelling as a framework for simulation and verification of the reliability of increasingly complex systems, and reports on experimental results related to a few select applications.

A bicategory of decorated cospans

- Mathematics
- 2016

If $\mathbf{C}$ is a category with pullbacks then there is a bicategory with the same objects as $\mathbf{C}$, spans as morphisms, and maps of spans as 2-morphisms, as shown by Benabou. Fong has…

25th Annual Computational Neuroscience Meeting: CNS-2016

- BiologyBMC Neuroscience
- 2016

Table of contents Functional advantages of cell-type heterogeneity in neural circuits, Dynamics and biomarkers of mental disorders, and Objective criteria for computational neuroscience model selection are presented.

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