Lyapunov Stability Analysis

소개

This skill provides specialized capabilities for understanding the qualitative behavior of differential equations and flows on manifolds. It enables Claude to perform rigorous stability analysis near equilibria and invariant sets, identify long-term global structures, and detect parameter-dependent bifurcations. Designed for researchers and engineers, it integrates with AlgebraicDynamics.jl for compositional modeling and utilizes a GF(3) triadic logic framework to ensure conserved transitions during complex system simulations.

주요 기능

• Evaluates global structure and long-term limit sets
• Integrates with AlgebraicDynamics.jl for resource-sharing machines
• Implements GF(3) conserved triadic composition logic
• Qualifies non-backtracking geodesic traversal via Möbius squarefree conditions
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• Analyzes local behavior near equilibria and invariant sets

사용 사례

• Verifying the robustness of control systems under perturbation
• Analyzing qualitative state changes and bifurcations in mathematical models
• Modeling compositional dynamical systems in Julia