Models and analyzes interacting dynamical systems using algebraic structures and GF(3) conservation principles.
The Coupled System skill provides a mathematical framework for understanding the qualitative behavior of differential equations and flows on manifolds within Claude. It specializes in compositional dynamical systems, allowing for the analysis of local equilibria, global structures, and parameter-dependent bifurcations. By integrating with AlgebraicDynamics.jl patterns and employing a triadic GF(3) logic, this skill enables researchers and developers to simulate resource-sharing machines and ensure structural consistency across complex, interacting mathematical models.
Key Features
01Maps global structures including long-term dynamics and limit sets
02Analyzes local behavior near equilibria and invariant sets
03Ensures GF(3) conservation (Trit -1) for stable system compositions
04Detects qualitative changes through parameter-dependent bifurcation analysis
058 GitHub stars
06Implements compositional dynamics via AlgebraicDynamics.jl integration
Use Cases
01Modeling complex feedback loops in biological or physical systems
02Conducting stability and robustness analysis under system perturbations
03Simulating resource-sharing machines in topological chemputing
