Analyzes dynamical systems to identify and model manifolds of points converging toward equilibrium states.
The Stable Manifold skill provides a specialized framework for dynamical systems theory, enabling Claude to assist with the qualitative behavior of differential equations and flows on manifolds. It excels at analyzing local behavior near equilibria, mapping global structures in phase space, and identifying bifurcations within complex systems. By integrating with AlgebraicDynamics.jl and utilizing GF(3) triadic composition, this skill allows for advanced modeling of chemical reaction networks and physical simulations where convergence and stability are critical.
Key Features
01Parameter-dependent bifurcation and stability analysis
02Analysis of equilibria and invariant sets in phase space
03Integration with AlgebraicDynamics.jl for compositional modeling
04Mapping of global structures and long-term limit sets
052 GitHub stars
06Support for non-backtracking geodesic traversal via Möbius filtering
Use Cases
01Analyzing stability and robustness in physical system simulations
02Modeling phase space convergence in chemical reaction networks
03Designing complex control systems using dynamical systems theory
