How does this skill integrate with Julia?

It provides specific patterns for using AlgebraicDynamics.jl, allowing the Lyapunov function to be treated as a compositional dynamical system.

What is the primary purpose of the Lyapunov Function skill?

It provides tools for understanding the qualitative behavior of differential equations, specifically focusing on how trajectories converge toward stable states or sinks.

What does the 'Trit -1' designation mean?

In the context of this skill's triadic logic (GF(3)), -1 represents sinks or absorbers, which are points in the system where trajectories aggregate.

Is this skill suitable for non-linear systems?

Yes, Lyapunov functions are a standard method for proving stability in non-linear dynamical systems where linear approximation may fail.

Lyapunov Function Analysis

Name: Lyapunov Function Analysis
Author: plurigrid

byplurigrid

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Data Science & ML

Analyzes the stability and qualitative behavior of dynamical systems using scalar function trajectories.

About

The Lyapunov Function skill empowers Claude to perform advanced stability analysis for complex dynamical systems and differential equations. By evaluating scalar functions that decrease along trajectories, it allows for the precise identification of sinks, absorbers, and invariant sets. This skill is particularly useful for researchers and engineers working with AlgebraicDynamics.jl, providing a framework for triadic composition and non-backtracking geodesic traversal to ensure robust, non-repeating system analysis within topological computing environments.

Key Features

Integrates with AlgebraicDynamics.jl for compositional modeling
Identifies global structures, long-term dynamics, and limit sets
Supports parameter-dependent bifurcation analysis
Analyzes local behavior near equilibria and invariant sets
Implements GF(3) triadic conservation for system state management
2 GitHub stars

Use Cases

Modeling resource-sharing machines in chemical or biological networks
Designing robust trajectories in topological chemputer simulations
Verifying the global asymptotic stability of control systems

About

Key Features

Integrates with AlgebraicDynamics.jl for compositional modeling
Identifies global structures, long-term dynamics, and limit sets
Supports parameter-dependent bifurcation analysis
Analyzes local behavior near equilibria and invariant sets
Implements GF(3) triadic conservation for system state management
2 GitHub stars

Use Cases

Modeling resource-sharing machines in chemical or biological networks
Designing robust trajectories in topological chemputer simulations
Verifying the global asymptotic stability of control systems