List of chaotic maps

In mathematics, a chaotic map is a map (= evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur in the study of dynamical systems.

Chaotic maps often generate fractals. Although a fractal may be constructed by an iterative procedure, some fractals are studied in and of themselves, as sets rather than in terms of the map that generates them. This is often because there are several different iterative procedures to generate the same fractal.

List of chaotic maps

Map Time domain Space domain Number of space dimensions Number of parameters Also known as
3-cells CNN system continuous real 3
2D circular chaotic map discrete real 2
2D Lorenz system  discrete real 2
2D Rational chaotic map  discrete rational 2
2D Van der Pol system  discrete real 2
ACT chaotic attractor  continuous real 3
Aizawa chaotic attractor  continuous real 3
Arneodo chaotic system continuous real 3
Arnold's cat map discrete real 2
Baker's map discrete real 2
Basin chaotic map discrete real 2
Bogdanov map discrete real 2
Brusselator continuous real 3
Burke-Shaw chaotic attractor continuous real 3
Chen chaotic attractor continuous real 3
Chen-Celikovsky system  continuous real 3
Chen-Lee system continuous real 3
Chossat-Golubitsky symmetry map
Chua circuit continuous real 3
Circle map discrete real 1
Complex quadratic map discrete complex 1 gives rise to the Mandelbrot set
Complex squaring map discretecomplex 1
Complex Cubic map
Clifford fractal map continuous real 3
Degenerate Double Rotor map
De Jong fractal map continuous real 3
Delayed-Logistic system discrete real 2
Double Rotor map
Duffing map discrete real 2 Holmes chaotic map
Duffing equation continuous real 1
Dyadic transformation discrete real 1 2x mod 1 map, Bernoulli map, doubling map, sawtooth map
Exponential map discrete complex 2
Feigenbaum strange nonchaotic map discrete real 3
Finance system continuous real 3
Folded-Towel hyperchaotic map continuous real 3
Fractal-Dream system discrete real 2
Gauss map discrete real 1 mouse map, Gaussian map
Generalized Baker map
Genesio-Tesi chaotic attractor continuous real 3
Grinch dragon fractal discrete real 2
Gumowski/Mira map discrete real 2
Hadley chaotic circulation continuous real 3
Half-inverted Rössler attractor
Halvorsen chaotic attractor continuous real 3
Hénon map discrete real 2
Hénon with 5th order polynomial
Hindmarsh-Rose neuronal model continuous real 3
Hitzl-Zele map
Horseshoe map discrete real 2
Hopa-Jong fractal discrete real 2
Hopalong orbit fractal discrete real 2
Hyper Logistic map discrete real 2
Hyperchaotic Chen system continuous real 3
Hyper Newton-Leipnik system continuous real 4
Hyper-Lorenz chaotic attractor continuous real 4
Hyper-Lu chaotic system continuous real 4
Hyper-Rössler chaotic attractor continuous real 4
Hyperchaotic attractor continuous real 4
Ikeda chaotic attractor continuous real 3
Ikeda map discrete real 2 Ikeda fractal map
Interval exchange map discrete real 1
Kaplan-Yorke map discrete real 2
Knot fractal map discrete real 2
Knot-Holder chaotic oscillator  continuous real 3
Lambić map  discrete discrete 1
Li symmetrical toroidal chaos  continuous real 3
Linear map on unit square
Logistic map discrete real 1 1
Lorenz attractor continuous real 3 3
Lorenz system's Poincare Return map
Lotka-Volterra system continuous real 3
Lozi map  discrete real 2
Moore-Spiegel chaotic oscillator  continuous real 3
Scroll-Attractor  continuous real 3
Jerk Circuit  continuous real 3
Newton-Leipnik system  continuous real 3
Nordmark truncated map
Nosé-Hoover system continuous real 3
Novel chaotic system  continuous real 3
Pickover fractal map  continuous real 3
Pomeau-Manneville maps for intermittent chaos discrete real 1 or 2 Normal-form maps for intermittency (Types I, II and III)
Polynom Type-A fractal map  continuous real 3 3
Polynom Type-B fractal map  continuous real 3 6
Polynom Type-C fractal map  continuous real 3 18
Pulsed rotor
Quadrup-Two orbit fractal  discrete real 2 3
Quasiperiodicity map
Rabinovich-Fabrikant chaotic attractor continuous real 3 2
Random Rotate map
Rayleigh-Benard chaotic oscillator continuous real 3 3
Rikitake chaotic attractor  continuous real 3 3
Rössler attractor continuous real 3 3
Rucklidge system  continuous real 3 2
Sakarya chaotic attractor  continuous real 3 2
Shaw-Pol chaotic oscillator  continuous real 3 3
Shimizu-Morioka system  continuous real 3 2
Shobu-Ose-Mori piecewise-linear map discrete real 1 piecewise-linear approximation for Pomeau-Manneville Type I map
Sinai map -
Sprott B chaotic system  continuous real 3 2
Sprott C chaotic system  continuous real 3 3
Sprott-Linz A chaotic attractor  continuous real 3 0
Sprott-Linz B chaotic attractor  continuous real 3 0
Sprott-Linz C chaotic attractor  continuous real 3 0
Sprott-Linz D chaotic attractor  continuous real 3 1
Sprott-Linz E chaotic attractor  continuous real 3 1
Sprott-Linz F chaotic attractor  continuous real 3 1
Sprott-Linz G chaotic attractor  continuous real 3 1
Sprott-Linz H chaotic attractor  continuous real 3 1
Sprott-Linz I chaotic attractor  continuous real 3 1
Sprott-Linz J chaotic attractor  continuous real 3 1
Sprott-Linz K chaotic system  continuous real 3 1
Sprott-Linz L chaotic attractor  continuous real 3 2
Sprott-Linz M chaotic attractor  continuous real 3 1
Sprott-Linz N chaotic attractor  continuous real 3 1
Sprott-Linz O chaotic attractor  continuous real 3 1
Sprott-Linz P chaotic attractor  continuous real 3 1
Sprott-Linz Q chaotic attractor  continuous real 3 2
Sprott-Linz R chaotic attractor  continuous real 3 2
Sprott-Linz S chaotic attractor  continuous real 3 1
Standard map, Kicked rotor discrete real 2 Chirikov standard map, Chirikov-Taylor map
Strizhak-Kawcynski chaotic oscillator  continuous real 3 9
Symmetric Flow attractor  continuous real 3 1
Symplectic map
Tangent map
Thomas' cyclically symmetric attractor  continuous real 3 1
Tent map discrete real 1
Tinkerbell map discrete real 2 4
Triangle map
Ueda chaotic oscillator  continuous real 3 3
Van der Pol oscillator continuous real 1 3
Willamowski-Rössler model  continuous real 3 10
WINDMI chaotic attractor  continuous real 1 2
Zaslavskii map discrete real 2
Zaslavskii rotation map