Working examples
The examples/ directory of the repository contains one Literate.jl script per model below; the pages of this section are generated from them and show the output of every step. The scripts are not part of the installed package. To run one yourself, install MappyDS together with a Makie backend and StaticArrays in any environment and include the script:
using Pkg
Pkg.add(["MappyDS", "CairoMakie", "StaticArrays"])
include("examples/duffing.jl")Each script builds the system, draws an orbit (with CairoMakie; the interactive viewer with GLMakie is shown in a non-executed block) and runs the numerical analysis: periodic points, their continuation, local bifurcations and bifurcation curves. They mirror the scripts of the Python package (see Python package); the mode names follow the Python scripts.
| Example | What it shows |
|---|---|
| Hénon map | A discrete map as a Diffeomorphism; the strange attractor, a bifurcation diagram and the maximum Lyapunov exponent from the Jacobian |
| Three coupled logistic maps | Fixed-point continuation in $\alpha$, multipliers along the branch, period-doubling curve in $(\alpha, \beta)$ |
| Izhikevich neuron | A 1-D Poincaré map with a firing reset; period doubling in $(a, I)$ |
| Forced Duffing oscillator | Stroboscopic map of a forced oscillator; the period doublings at $B \approx 0.171687$ and $0.368655$ |
| Forced Alpazur oscillator | A piecewise-smooth system with hysteresis and two end modes; period doubling in $(V, B_1)$ |
The hybrid-system examples reproduce figures of Miino [1].