Catalog
Discrete maps
Each map gets a definition, defining equations, parameter intervals where chaos occurs, characteristic Lyapunov exponent, and history.
1D maps
Single state variable, classical chaos toolbox.
- Logistic mapdim 1
Robert May's 1976 review introduced this one-parameter quadratic family as the canonical example of complex dynamics from simple rules.
- Tent mapdim 1
Piecewise-linear cousin of the logistic map with the same topological structure but no quadratic curvature.
- Sine mapdim 1
Topologically equivalent to the logistic in the chaotic regime; the smoothness changes critical exponents in transient analysis.
- Bernoulli (doubling) mapdim 1
Mod-1 doubling.
- Gauss (mouse) mapdim 1
Sometimes called the 'mouse map' for its characteristic shape.
- Chebyshev mapdim 1
The k-th Chebyshev polynomial T_k applied iteratively.
- PWLCM (piecewise-linear chaotic map)dim 1
A workhorse of chaos-based cryptography: simple, fast, uniform invariant density, large positive Lyapunov exponent, and parameter p easy to use as a key..
- Circle mapdim 1
Arnold's standard form for the iterates of a circle homeomorphism with a sinusoidal nonlinearity.
2D maps
Hénon-like, area-preserving, optical, mechanical.
- Standard (Chirikov) mapdim 2
Chirikov's twist map of a kicked rotator.
- Hénon mapdim 2
Hénon's 1976 reduction of the Lorenz system.
- Lozi mapdim 2
Piecewise-linear variant of Hénon.
- Arnold cat mapdim 2
Toral automorphism with eigenvalues (3 ± √5)/2.
- Baker's mapdim 2
A simple model of mixing: bake the dough by stretching and folding.
- Ikeda mapdim 2
Ikeda's 1979 model of light in a ring cavity.
- Tinkerbell mapdim 2
A 4-parameter discrete dynamical system whose attractor is dragon-like and notoriously sensitive to parameters..
- Gingerbreadman mapdim 2
A piecewise-linear area-preserving 2D map whose iterates trace out a gingerbread-man silhouette around a regular pattern of fixed points..
- Zaslavsky mapdim 2
Dissipative twist map generalising the standard map.
- Duffing map (discrete)dim 2
Discrete analogue of the Duffing oscillator.
Coupled maps & lattices
Many maps interacting; spatiotemporal chaos.