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[1] | discrete | real | 2 | 1 | |
| 2D Lorenz system [2] | discrete | real | 2 | 1 | |
| 2D Rational chaotic map [3] | discrete | rational | 2 | 2 | |
| Van der Pol system [4] | continuous | real | 2 | 2 | |
| ACT chaotic attractor [5] | continuous | real | 3 | ||
| Aizawa chaotic attractor [6] | continuous | real | 3 | ||
| Arneodo chaotic system[7] | continuous | real | 3 | ||
| Arnold's cat map | discrete | real | 2 | 0 | |
| Baker's map | discrete | real | 2 | 0 | |
| Basin chaotic map[8] | discrete | real | 2 | ||
| Beta Chaotic Map [9] | 12 | ||||
| Bogdanov map | discrete | real | 2 | 3 | |
| Brusselator | continuous | real | 3 | ||
| Burke-Shaw chaotic attractor[10] | continuous | real | 3 | 2 | |
| Chen chaotic attractor[11] | continuous | real | 3 | ||
| Chen-Celikovsky system [12] | continuous | real | 3 | ||
| Chen-Lee system | continuous | real | 3 | ||
| Chossat-Golubitsky symmetry map | |||||
| Chua circuit[13] | continuous | real | 3 | 3 | |
| Circle map | discrete | real | 1 | 2 | |
| Complex quadratic map | discrete | complex | 1 | 1 | gives rise to the Mandelbrot set |
| Complex squaring map | discrete | complex | 1 | 0 | acts on the Julia set for the squaring map. |
| Complex cubic map | discrete | complex | 1 | 2 | |
| Clifford fractal map[14] | discrete | real | 2 | 4 | |
| Degenerate Double Rotor map | |||||
| De Jong fractal map[15] | discrete | real | 2 | 4 | |
| Delayed-Logistic system[16] | discrete | real | 2 | 1 | |
| Double rotor map | |||||
| Duffing map | discrete | real | 2 | 2 | Holmes chaotic map |
| Duffing equation | continuous | real | 2 | 5 (3 independent) | |
| Dyadic transformation | discrete | real | 1 | 0 | 2x mod 1 map, Bernoulli map, doubling map, sawtooth map |
| Exponential map | discrete | complex | 2 | 1 | |
| Feigenbaum strange nonchaotic map[17] | discrete | real | 3 | ||
| Finance system[18] | continuous | real | 3 | ||
| Folded-Towel hyperchaotic map[19] | continuous | real | 3 | ||
| Fractal-Dream system[20] | discrete | real | 2 | ||
| Gauss map | discrete | real | 1 | mouse map, Gaussian map | |
| Generalized Baker map | |||||
| Genesio-Tesi chaotic attractor[21] | continuous | real | 3 | ||
| Gingerbreadman map[22] | discrete | real | 2 | ||
| Grinch dragon fractal | discrete | real | 2 | ||
| Gumowski/Mira map[23] | discrete | real | 2 | ||
| Hadley chaotic circulation | continuous | real | 3 | 0 | |
| Half-inverted Rössler attractor[24] | |||||
| Halvorsen chaotic attractor[25] | continuous | real | 3 | ||
| Hénon map | discrete | real | 2 | 2 | |
| Hénon with 5th order polynomial | |||||
| Hindmarsh-Rose neuronal model | continuous | real | 3 | 8 | |
| Hitzl-Zele map | |||||
| Horseshoe map | discrete | real | 2 | 1 | |
| Hopa-Jong fractal[26] | discrete | real | 2 | ||
| Hopalong orbit fractal[27] | discrete | real | 2 | ||
| Hyper Logistic map[28] | discrete | real | 2 | ||
| Hyperchaotic Chen system[29] | continuous | real | 3 | ||
| Hyper Newton-Leipnik system | continuous | real | 4 | ||
| Hyper-Lorenz chaotic attractor | continuous | real | 4 | ||
| Hyper-Lu chaotic system[30] | continuous | real | 4 | ||
| Hyper-Rössler chaotic attractor[31] | continuous | real | 4 | ||
| Hyperchaotic attractor[32] | continuous | real | 4 | ||
| Ikeda chaotic attractor[33] | continuous | real | 3 | ||
| Ikeda map | discrete | real | 2 | 3 | Ikeda fractal map |
| Interval exchange map | discrete | real | 1 | variable | |
| Kaplan-Yorke map | discrete | real | 2 | 1 | |
| Knot fractal map[34] | discrete | real | 2 | ||
| Knot-Holder chaotic oscillator [35] | continuous | real | 3 | ||
| Kuramoto–Sivashinsky equation | continuous | real | |||
| Lambić map [36] | discrete | discrete | 1 | ||
| Li symmetrical toroidal chaos [37] | continuous | real | 3 | ||
| Linear map on unit square | |||||
| Logistic map | discrete | real | 1 | 1 | |
| Lorenz system | continuous | real | 3 | 3 | |
| Lorenz system's Poincaré return map | discrete | real | 2 | 3 | |
| Lorenz 96 model | continuous | real | arbitrary | 1 | |
| Lotka-Volterra system | continuous | real | 3 | 4 | |
| Lozi map [38] | discrete | real | 2 | ||
| Moore-Spiegel chaotic oscillator [39] | continuous | real | 3 | ||
| Scroll-Attractor [40] | continuous | real | 3 | ||
| Jerk Circuit [41] | continuous | real | 3 | ||
| Newton-Leipnik system | continuous | real | 3 | ||
| Nordmark truncated map | |||||
| Nosé-Hoover system | continuous | real | 3 | ||
| Novel chaotic system [42] | continuous | real | 3 | ||
| Pickover fractal map [43] | 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 [44] | continuous | real | 3 | 3 | |
| Polynom Type-B fractal map [45] | continuous | real | 3 | 6 | |
| Polynom Type-C fractal map [46] | continuous | real | 3 | 18 | |
| Pulsed rotor | |||||
| Quadrup-Two orbit fractal [47] | discrete | real | 2 | 3 | |
| Quasiperiodicity map | |||||
| Mikhail Anatoly chaotic attractor | continuous | real | 3 | 2 | |
| Random Rotate map | |||||
| Rayleigh-Benard chaotic oscillator | continuous | real | 3 | 3 | |
| Rikitake chaotic attractor [48] | continuous | real | 3 | 3 | |
| Rössler attractor | continuous | real | 3 | 3 | |
| Rucklidge system [49] | continuous | real | 3 | 2 | |
| Sakarya chaotic attractor [50] | continuous | real | 3 | 2 | |
| Shaw-Pol chaotic oscillator [51][52] | continuous | real | 3 | 3 | |
| Shimizu-Morioka system [53] | 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 [54][55] | continuous | real | 3 | 2 | |
| Sprott C chaotic system [56][57] | continuous | real | 3 | 3 | |
| Sprott-Linz A chaotic attractor [58][59][60] | continuous | real | 3 | 0 | |
| Sprott-Linz B chaotic attractor [61][62][63] | continuous | real | 3 | 0 | |
| Sprott-Linz C chaotic attractor [64][65][66] | continuous | real | 3 | 0 | |
| Sprott-Linz D chaotic attractor [67][68][69] | continuous | real | 3 | 1 | |
| Sprott-Linz E chaotic attractor [70][71][72] | continuous | real | 3 | 1 | |
| Sprott-Linz F chaotic attractor [73][74][75] | continuous | real | 3 | 1 | |
| Sprott-Linz G chaotic attractor [76][77][78] | continuous | real | 3 | 1 | |
| Sprott-Linz H chaotic attractor [79][80][81] | continuous | real | 3 | 1 | |
| Sprott-Linz I chaotic attractor [82][83][84] | continuous | real | 3 | 1 | |
| Sprott-Linz J chaotic attractor [85][86][87] | continuous | real | 3 | 1 | |
| Sprott-Linz K chaotic attractor [88][89][90] | continuous | real | 3 | 1 | |
| Sprott-Linz L chaotic attractor [91][92][93] | continuous | real | 3 | 2 | |
| Sprott-Linz M chaotic attractor [94][95][96] | continuous | real | 3 | 1 | |
| Sprott-Linz N chaotic attractor [97][98][99] | continuous | real | 3 | 1 | |
| Sprott-Linz O chaotic attractor [100][101][102] | continuous | real | 3 | 1 | |
| Sprott-Linz P chaotic attractor [103][104][105] | continuous | real | 3 | 1 | |
| Sprott-Linz Q chaotic attractor [106][107][108] | continuous | real | 3 | 2 | |
| Sprott-Linz R chaotic attractor [109][110][111] | continuous | real | 3 | 2 | |
| Sprott-Linz S chaotic attractor [112][113][114] | continuous | real | 3 | 1 | |
| Standard map, Kicked rotor | discrete | real | 2 | 1 | Chirikov standard map, Chirikov-Taylor map |
| Strizhak-Kawczynski chaotic oscillator [115][116] | continuous | real | 3 | 9 | |
| Symmetric Flow attractor [117] | continuous | real | 3 | 1 | |
| Symplectic map | |||||
| Tangent map | |||||
| Thomas' cyclically symmetric attractor [118] | continuous | real | 3 | 1 | |
| Tent map | discrete | real | 1 | ||
| Tinkerbell map | discrete | real | 2 | 4 | |
| Triangle map | |||||
| Ueda chaotic oscillator [119] | continuous | real | 3 | 3 | |
| Van der Pol oscillator | continuous | real | 1 | 3 | |
| Willamowski-Rössler model [120] | continuous | real | 3 | 10 | |
| WINDMI chaotic attractor [121][122][123] | continuous | real | 1 | 2 | |
| Zaslavskii map | discrete | real | 2 | 4 | |
| Zaslavskii rotation map | |||||
| Zeraoulia-Sprott map [124] | discrete | real | 2 | 2 | |
List of fractals
- Cantor set
- de Rham curve
- Gravity set, or Mitchell-Green gravity set
- Julia set - derived from complex quadratic map
- Koch snowflake - special case of de Rham curve
- Lyapunov fractal
- Mandelbrot set - derived from complex quadratic map
- Menger sponge
- Newton fractal
- Nova fractal - derived from Newton fractal
- Quaternionic fractal - three dimensional complex quadratic map
- Sierpinski carpet
- Sierpinski triangle
References
- Chaos from Euler Solution of ODEs
- Chaos from Euler Solution of ODEs
- On the dynamics of a new simple 2-D rational discrete mapping
- Chaos from Euler Solution of ODEs
- http://www.yangsky.us/ijcc/pdf/ijcc83/IJCC823.pdf%5B%5D
- The Aizawa attractor
- Local Stability and Hopf Bifurcation Analysis of the Arneodo’s System
- Basin of attraction Archived 2014-07-01 at the Wayback Machine
- Image encryption based on new Beta chaotic maps
- 1981 The Burke & Shaw system
- A new chaotic attractor coined
- A new chaotic attractor coined
- http://www.scholarpedia.org/article/Chua_circuit Chua Circuit
- Clifford Attractors
- Peter de Jong Attractors
- A discrete population model of delayed regulation
- Irregular Attractors
- A New Finance Chaotic Attractor
- Hyperchaos Archived 2015-12-22 at the Wayback Machine
- Visions of Chaos 2D Strange Attractor Tutorial
- A new chaotic system and beyond: The generalized Lorenz-like system
- Gingerbreadman map
- Mira Fractals
- Half-inverted tearing
- Halvorsen: A tribute to Dr. Edward Norton Lorenz
- Peter de Jong Attractors
- Hopalong orbit fractal
- Irregular Attractors
- Global chaos synchronization of hyperchaotic chen system by sliding model control
- Hyper-Lu system
- The first hyperchaotic system
- Hyperchaotic attractor Archived 2015-12-22 at the Wayback Machine
- Attractors
- Knot fractal map Archived 2015-12-22 at the Wayback Machine
- A new discrete chaotic map based on the composition of permutations
- A 3D symmetrical toroidal chaos
- Lozi maps
- Moore-Spiegel Attractor
- A new chaotic system and beyond: The generalized lorenz-like system
- A New Chaotic Jerk Circuit
- Chaos Control and Hybrid Projective Synchronization of a Novel Chaotic System
- Pickover
- Polynomial Type-A
- Polynomial Type-B
- Polynomial Type-C
- Quadrup Two Orbit Fractal
- Rikitake chaotic attractor Archived 2010-06-20 at the Wayback Machine
- Description of strange attractors using invariants of phase-plane
- Skarya Archived 2015-12-22 at the Wayback Machine
- Van der Pol Oscillator Equations
- Shaw-Pol chaotic oscillator Archived 2015-12-22 at the Wayback Machine
- The Shimiziu-Morioka System
- Sprott B chaotic attractor Archived 2007-02-27 at the Wayback Machine
- Chaos Blog - Sprott B system Archived 2015-12-22 at the Wayback Machine
- Sprott C chaotic attractor Archived 2007-02-27 at the Wayback Machine
- Chaos Blog - Sprott C system Archived 2015-12-22 at the Wayback Machine
- Sprott's Gateway - Sprott-Linz A chaotic attractor Archived 2007-02-27 at the Wayback Machine
- A new chaotic system and beyond: The generalized Lorenz-like System
- Chaos Blog - Sprott-Linz A chaotic attractor Archived 2015-12-22 at the Wayback Machine
- Sprott's Gateway - Sprott-Linz B chaotic attractor Archived 2007-02-27 at the Wayback Machine
- A new chaotic system and beyond: The generalized Lorenz-like System
- Chaos Blog - Sprott-Linz B chaotic attractor Archived 2015-12-22 at the Wayback Machine
- Sprott's Gateway - Sprott-Linz C chaotic attractor Archived 2007-02-27 at the Wayback Machine
- A new chaotic system and beyond: The generalized Lorenz-like System
- Chaos Blog - Sprott-Linz C chaotic attractor Archived 2015-12-22 at the Wayback Machine
- Sprott's Gateway - Sprott-Linz D chaotic attractor Archived 2007-02-27 at the Wayback Machine
- A new chaotic system and beyond: The generalized Lorenz-like System
- Chaos Blog - Sprott-Linz D chaotic attractor Archived 2015-12-22 at the Wayback Machine
- Sprott's Gateway - Sprott-Linz E chaotic attractor Archived 2007-02-27 at the Wayback Machine
- A new chaotic system and beyond: The generalized Lorenz-like System
- Chaos Blog - Sprott-Linz E chaotic attractor Archived 2015-12-22 at the Wayback Machine
- Sprott's Gateway - Sprott-Linz F chaotic attractor Archived 2007-02-27 at the Wayback Machine
- A new chaotic system and beyond: The generalized Lorenz-like System
- Chaos Blog - Sprott-Linz F chaotic attractor Archived 2015-12-22 at the Wayback Machine
- Sprott's Gateway - Sprott-Linz G chaotic attractor Archived 2007-02-27 at the Wayback Machine
- A new chaotic system and beyond: The generalized Lorenz-like System
- Chaos Blog - Sprott-Linz G chaotic attractor Archived 2015-12-22 at the Wayback Machine
- Sprott's Gateway - Sprott-Linz H chaotic attractor Archived 2007-02-27 at the Wayback Machine
- A new chaotic system and beyond: The generalized Lorenz-like System
- Chaos Blog - Sprott-Linz H chaotic attractor Archived 2015-12-22 at the Wayback Machine
- Sprott's Gateway - Sprott-Linz I chaotic attractor Archived 2007-02-27 at the Wayback Machine
- A new chaotic system and beyond: The generalized Lorenz-like System
- Chaos Blog - Sprott-Linz I chaotic attractor Archived 2015-12-22 at the Wayback Machine
- Sprott's Gateway - Sprott-Linz J chaotic attractor Archived 2007-02-27 at the Wayback Machine
- A new chaotic system and beyond: The generalized Lorenz-like System
- Chaos Blog - Sprott-Linz J chaotic attractor Archived 2015-12-22 at the Wayback Machine
- Sprott's Gateway - Sprott-Linz K chaotic attractor Archived 2007-02-27 at the Wayback Machine
- A new chaotic system and beyond: The generalized Lorenz-like System
- Chaos Blog - Sprott-Linz K chaotic attractor Archived 2015-12-22 at the Wayback Machine
- Sprott's Gateway - Sprott-Linz L chaotic attractor Archived 2007-02-27 at the Wayback Machine
- A new chaotic system and beyond: The generalized Lorenz-like System
- Chaos Blog - Sprott-Linz L chaotic attractor Archived 2015-12-22 at the Wayback Machine
- Sprott's Gateway - Sprott-Linz M chaotic attractor Archived 2007-02-27 at the Wayback Machine
- A new chaotic system and beyond: The generalized Lorenz-like System
- Chaos Blog - Sprott-Linz M chaotic attractor Archived 2015-12-22 at the Wayback Machine
- Sprott's Gateway - Sprott-Linz N chaotic attractor Archived 2007-02-27 at the Wayback Machine
- A new chaotic system and beyond: The generalized Lorenz-like System
- Chaos Blog - Sprott-Linz N chaotic attractor Archived 2015-12-22 at the Wayback Machine
- Sprott's Gateway - Sprott-Linz O chaotic attractor Archived 2007-02-27 at the Wayback Machine
- A new chaotic system and beyond: The generalized Lorenz-like System
- Chaos Blog - Sprott-Linz O chaotic attractor Archived 2015-12-22 at the Wayback Machine
- Sprott's Gateway - Sprott-Linz P chaotic attractor Archived 2007-02-27 at the Wayback Machine
- A new chaotic system and beyond: The generalized Lorenz-like System
- Chaos Blog - Sprott-Linz P chaotic attractor Archived 2015-12-22 at the Wayback Machine
- Sprott's Gateway - Sprott-Linz Q chaotic attractor Archived 2007-02-27 at the Wayback Machine
- A new chaotic system and beyond: The generalized Lorenz-like System
- Chaos Blog - Sprott-Linz Q chaotic attractor Archived 2015-12-22 at the Wayback Machine
- Sprott's Gateway - Sprott-Linz R chaotic attractor Archived 2007-02-27 at the Wayback Machine
- A new chaotic system and beyond: The generalized Lorenz-like System
- Chaos Blog - Sprott-Linz R chaotic attractor Archived 2015-12-22 at the Wayback Machine
- Sprott's Gateway - Sprott-Linz S chaotic attractor Archived 2007-02-27 at the Wayback Machine
- A new chaotic system and beyond: The generalized Lorenz-like System
- Chaos Blog - Sprott-Linz S chaotic attractor Archived 2015-12-22 at the Wayback Machine
- Strizhak-Kawczynski chaotic oscillator
- Chaos Blog - Strizhak-Kawczynski chaotic oscillator Archived 2015-12-22 at the Wayback Machine
- Sprott's Gateway - A symmetric chaotic flow
- http://sprott.physics.wisc.edu/chaostsa/ Sprott's Gateway - Chaos and Time-Series Analysis
- Oscillator of Ueda
- Internal fluctuations in a model of chemical chaos
- Synchronization of Chaotic Fractional-Order WINDMI Systems via Linear State Error Feedback Control
- Adaptive Backstepping Controller Design for the Anti-Synchronization of Identical WINDMI Chaotic Systems with Unknown Parameters and its SPICE Implementation
- Chen, Guanrong; Kudryashova, Elena V.; Kuznetsov, Nikolay V.; Leonov, Gennady A. (2016). "Dynamics of the Zeraoulia–Sprott Map Revisited". International Journal of Bifurcation and Chaos. 26 (7): 1650126–21. arXiv:1602.08632. Bibcode:2016IJBC...2650126C. doi:10.1142/S0218127416501261.
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