For decades we have developed beautiful mathematical models for specific domains: the Lorenz attractor, Navier–Stokes equations, Lotka–Volterra systems, Mackey–Glass, neural networks, financial models and many more. Each describes a particular phenomenon remarkably well, yet they often feel isolated from one another.
Compositional Dynamics is an experimental idea based on a simple question:
What if many dynamical systems are built from the same small set of reusable dynamical primitives?
Instead of starting with equations, we start with mechanisms. Possible primitives could include:
- drive
- damp
- delay
- echo
- modulate
- couple
- reflect
- threshold
- noise
Known systems could then be viewed as different compositions of these primitives rather than entirely different mathematical objects. This perspective is inspired by both System Dynamics, which models systems through feedback loops, delays and stocks, and Category Theory, which studies how complex structures emerge through composition.
The goal is not to replace existing mathematics. Instead, the goal is to build a common language for dynamical systems and explore whether similar compositions lead to similar behaviors.
A possible playground would allow researchers to visually compose primitive operators, simulate the resulting dynamics and compare them with known toy models. Over time, one could build a library of dynamical fingerprints, explore parameter spaces and investigate where systems become unstable, oscillatory or chaotic.
Whether this ultimately becomes a useful framework remains an open question. But even if it does not, exploring dynamical systems from a compositional perspective may reveal interesting structural similarities that are difficult to see when looking only at equations.
References
- System Dynamics
- Category Theory
- Dynamical Systems
- Chaos Theory
- Reservoir Computing
- Assembly Theory