Lyapunov Characteristic Exponents In Rock-Paper-Scissors Game

Compute Lyapunov Characteristic Exponents (LCEs) for the pestilent Rock–Paper–Scissors (RPS) mean-field ODE model.
It uses a Benettin-style algorithm with Gram–Schmidt reorthonormalization and a 4th-order Runge–Kutta (RK4) integrator, and supports parameter sweeps in the pest strength q.

• Core language: C
• Automation: Bash (run.sh)
• Plots: gnuplot + LaTeX (pdflatex/lualatex)

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Repository structure

├── run.sh                 # main driver: sweeps q and runs (LCE/BIF/PLT) keys
├── makefile               # builds cp.out, lz.out, sn.out, sd.out
├── lce.h                  # model + numerical presets (ntr, nit, ipb, pa, pb=q, pc, x0,y0,z0)
├── src/
│   ├── lz.c               # main LCE computation + trajectory output
│   ├── cp.c               # critical points extractor (for bifurcation diagrams)
│   ├── sn.c               # sorts LCE output by q
│   ├── sd.c               # mean/std helper (GSL)
│   └── *.plt              # plotting scripts (gnuplot)
├── dat/                   # generated data files (.dat)
│   └── ps/                # per-q trajectories
└── plt/                   # generated figures (.pdf / .png)
    └── ps/                # per-q plots

Quick Start

Inputs and presets

All default parameters are defined in lce.h, including:

• ntr : transient iterations discarded in the LCE accumulation
• nit : iterations used for averaging
• ipb : inner RK steps between reorthonormalizations
• pa, pb, pc : model parameters (pb = q)
• x0, y0, z0 : initial conditions

Running

1. Give execution permission to the main script:

chmod +x run.sh

2. Choose a range for the pest strength q:

./run.sh 0.82 0.99 0.001

Important

at the top of run.sh there are three keys: LCE, BIF, PLT.

• LCE=1: Computes trajectories and appends LCEs into dat/lce.dat for each q.
• BIF=1: Extracts critical points from trajectories and generates bifurcation datasets.
• PLT=1: Produces phase-space, bifurcation diagram and LCE plots using gnuplot + LaTeX.