Jacobian Linearization

소개

The Jacobian skill provides Claude with specialized capabilities in dynamical systems theory, focusing on the construction and analysis of partial derivative matrices. It enables the linearization of non-linear differential equations near equilibrium points, allowing for a qualitative assessment of flows on manifolds. This skill is particularly useful for identifying system sinks and absorbers (Trit -1), analyzing bifurcations, and evaluating the long-term stability of complex models. It integrates seamlessly with compositional frameworks like AlgebraicDynamics.jl and utilizes GF(3) triadic logic for conserved system states.

주요 기능

• Integrates with AlgebraicDynamics.jl for compositional modeling
• Computes matrices of partial derivatives for system linearization
• Analyzes local behavior near equilibria and invariant sets
• 2 GitHub stars
• Identifies sinks and absorbers within a GF(3) triadic framework
• Supports non-backtracking geodesic traversal via Möbius filtering

사용 사례

• Modeling resource-sharing machines in compositional dynamical systems
• Detecting parameter-dependent bifurcations in complex dynamical flows
• Evaluating the stability of a physical or biological system at equilibrium