Stable Manifold Analysis

About

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

• Parameter-dependent bifurcation and stability analysis
• Analysis of equilibria and invariant sets in phase space
• Integration with AlgebraicDynamics.jl for compositional modeling
• Mapping of global structures and long-term limit sets
• 2 GitHub stars
• Support for non-backtracking geodesic traversal via Möbius filtering

Use Cases

• Analyzing stability and robustness in physical system simulations
• Modeling phase space convergence in chemical reaction networks
• Designing complex control systems using dynamical systems theory