[phase-diagram] Phase Diagram (State Space Plot)

[MarkusNeusinger]

A phase diagram or state space plot displays the trajectory of a dynamical system by plotting a variable against its derivative (x vs dx/dt), useful for analyzing oscillators, pendulums, and other physical systems.

[claude]

✅ Spec ID: phase-diagram

Rationale: This is a distinct plot type for dynamical systems analysis, showing trajectories in state space (x vs dx/dt). It's different from vector field plots like quiver or streamline since it specifically visualizes solution trajectories of differential equations.

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[github-actions]

✅ Specification Ready: phase-diagram

PR: #3006

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specification.md

phase-diagram: Phase Diagram (State Space Plot)

Description

A phase diagram (or state space plot) displays the trajectory of a dynamical system by plotting a variable against its derivative (x vs dx/dt). This visualization reveals the qualitative behavior of systems including fixed points, limit cycles, stability, and oscillation patterns. It is essential for analyzing differential equations without solving them explicitly.

Applications

• Analyzing simple harmonic oscillators and damped pendulum motion in physics education
• Studying predator-prey dynamics (Lotka-Volterra equations) in ecology
• Examining stability of electrical circuits with inductors and capacitors
• Visualizing attractors and bifurcations in nonlinear dynamics research

Data

• x (numeric array) - Position or state variable values along the trajectory
• dx_dt (numeric array) - Derivative (velocity) values corresponding to each x
• t (numeric array, optional) - Time values for computing derivatives from raw position data
• Size: 200-2000 points for smooth trajectories
• Example: A simple pendulum with initial displacement, showing spiral convergence to equilibrium

Notes

• Multiple trajectories from different initial conditions can reveal basin of attraction structure
• Fixed points (equilibria) occur where the trajectory crosses dx/dt = 0
• Closed loops indicate periodic oscillation (limit cycles or centers)
• Consider adding direction arrows or color gradient to show time evolution
• For damped systems, trajectories spiral inward; for driven systems, they may form limit cycles

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[github-actions]

🚀 Specification Merged!

Specification: phase-diagram
PR: #3006 (merged)

The specification is now in main and synced to PostgreSQL.

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Available libraries: matplotlib, seaborn, plotly, bokeh, altair, plotnine, pygal, highcharts, letsplot

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