Nonlinear Systems

Collection of Python scripts that simulate nonlinear systems.

Description

• Lorenz.py - Generates a randomized Lorenz system.
• LorenzRK4vsEuler.py - Compares along a time series the divergence of the Lorenz system given the same initial conditions where one is solved through RK4 integration and the other by first order Euler integration.
• aniLorenz.py - An animataed graph of the behavior of the Lorenz system.
• doublePend.py - Animated graph of a double pendulum's state.
• doublePendNoPhase.py - Double pendulum simulation.
• gravRand.py - Randomized n-body problem.
• gravRandHackyTrack.py - Uses a "hacky" trick that adds dampening when two particles get too close.
• gravRandMap.py - Creates a phase-space-like map of an entire 3-body system.
• gravRandMapPregen.py - Generates a non-animated map of a 3-body system.
• gravRandTrack.py - Tracks a single particle in an n-body system.
• logisticdifference.py - Graphs the logistic difference equation.
• logisticmap.py - Maps the behavior of the logistic difference equation on a map, creating the famous logistic map.
• lorenz2D.py - Maps only part of the lorenz system such that we get a 2D slice.
• lorenzRK4.py - Lorenz system integrated using RK4.
• lorenzTimeSeries.py - The Lorenz system along a time series.
• lorenzrayleigh.py - Graphs the Lorenz system's behavior given different values for Rayleigh's number. Shows the exact point that "chaos" occurs for given parameters.
• lorenzrayleighNoSettle.py - Graphs the Lorenz system's behavior without letting it settle first given different values for Rayleigh's number.
• multiLorenz.py - Graphs multiple random lorenz systems side by side.
• pendWithDrag.py - Demonstrates a common pendulum system with drag and phase plane.
• simplePend.py - Demonstrates a common pendulum system without drag and phase plane.
• simplePendNoPhase.py - Demonstrates a simple pendulum without a phase plane.

Dependencies

• Matplotlib
• Numpy
• Python 3

Authors

Kamran Haq

Acknowledgments

https://docs.google.com/document/d/1wrI7gFVG9qeUy9F4y6L_Zpeql7y2ohRpxAKAplZOfh0/edit?usp=sharing