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
2D Lorenz system [2]	discrete	real	2
2D Rational chaotic map [3]	discrete	rational	2
2D Van der Pol system [4]	discrete	real	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
Baker's map	discrete	real	2
Basin chaotic map[8]	discrete	real	2
Bogdanov map	discrete	real	2
Brusselator	continuous	real	3
Burke-Shaw chaotic attractor[9]	continuous	real	3
Chen chaotic attractor[10]	continuous	real	3
Chen-Celikovsky system [11]	continuous	real	3
Chen-Lee system	continuous	real	3
Chossat-Golubitsky symmetry map
Chua circuit[12]	continuous	real	3
Circle map	discrete	real	1
Complex quadratic map	discrete	complex	1		gives rise to the Mandelbrot set
Complex squaring map	discrete	complex	1
Complex Cubic map
Clifford fractal map[13]	continuous	real	3
Degenerate Double Rotor map
De Jong fractal map[14]	continuous	real	3
Delayed-Logistic system[15]	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[16]	discrete	real	3
Finance system[17]	continuous	real	3
Folded-Towel hyperchaotic map[18]	continuous	real	3
Fractal-Dream system[19]	discrete	real	2
Gauss map	discrete	real	1		mouse map, Gaussian map
Generalized Baker map
Genesio-Tesi chaotic attractor[20]	continuous	real	3
Gingerbreadman map[21]	discrete	real	2
Grinch dragon fractal	discrete	real	2
Gumowski/Mira map[22]	discrete	real	2
Hadley chaotic circulation	continuous	real	3
Half-inverted Rössler attractor[23]
Halvorsen chaotic attractor[24]	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[25]	discrete	real	2
Hopalong orbit fractal[26]	discrete	real	2
Hyper Logistic map[27]	discrete	real	2
Hyperchaotic Chen system[28]	continuous	real	3
Hyper Newton-Leipnik system[29]	continuous	real	4
Hyper-Lorenz chaotic attractor[30]	continuous	real	4
Hyper-Lu chaotic system[31]	continuous	real	4
Hyper-Rössler chaotic attractor[32]	continuous	real	4
Hyperchaotic attractor[33]	continuous	real	4
Ikeda chaotic attractor[34]	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[35]	discrete	real	2
Knot-Holder chaotic oscillator [36]	continuous	real	3
Lambić map [37]	discrete	discrete	1
Li symmetrical toroidal chaos [38]	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 [39]	discrete	real	2
Moore-Spiegel chaotic oscillator [40]	continuous	real	3
Scroll-Attractor [41]	continuous	real	3
Jerk Circuit [42]	continuous	real	3
Newton-Leipnik system [43]	continuous	real	3
Nordmark truncated map
Nosé-Hoover system	continuous	real	3
Novel chaotic system [44]	continuous	real	3
Pickover fractal map [45]	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 [46]	continuous	real	3	3
Polynom Type-B fractal map [47]	continuous	real	3	6
Polynom Type-C fractal map [48]	continuous	real	3	18
Pulsed rotor
Quadrup-Two orbit fractal [49]	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 [50]	continuous	real	3	3
Rössler attractor	continuous	real	3	3
Rucklidge system [51]	continuous	real	3		2
Sakarya chaotic attractor [52]	continuous	real	3	2
Shaw-Pol chaotic oscillator [53][54]	continuous	real	3	3
Shimizu-Morioka system [55]	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 [56][57]	continuous	real	3	2
Sprott C chaotic system [58][59]	continuous	real	3	3
Sprott-Linz A chaotic attractor [60][61][62]	continuous	real	3	0
Sprott-Linz B chaotic attractor [63][64][65]	continuous	real	3	0
Sprott-Linz C chaotic attractor [66][67][68]	continuous	real	3	0
Sprott-Linz D chaotic attractor [69][70][71]	continuous	real	3	1
Sprott-Linz E chaotic attractor [72][73][74]	continuous	real	3	1
Sprott-Linz F chaotic attractor [75][76][77]	continuous	real	3	1
Sprott-Linz G chaotic attractor [78][79][80]	continuous	real	3	1
Sprott-Linz H chaotic attractor [81][82][83]	continuous	real	3	1
Sprott-Linz I chaotic attractor [84][85][86]	continuous	real	3	1
Sprott-Linz J chaotic attractor [87][88][89]	continuous	real	3	1
Sprott-Linz K chaotic system [90][91][92]	continuous	real	3	1
Sprott-Linz L chaotic attractor [93][94][95]	continuous	real	3	2
Sprott-Linz M chaotic attractor [96][97][98]	continuous	real	3	1
Sprott-Linz N chaotic attractor [99][100][101]	continuous	real	3	1
Sprott-Linz O chaotic attractor [102][103][104]	continuous	real	3	1
Sprott-Linz P chaotic attractor [105][106][107]	continuous	real	3	1
Sprott-Linz Q chaotic attractor [108][109][110]	continuous	real	3	2
Sprott-Linz R chaotic attractor [111][112][113]	continuous	real	3	2
Sprott-Linz S chaotic attractor [114][115][116]	continuous	real	3	1
Standard map, Kicked rotor	discrete	real	2		Chirikov standard map, Chirikov-Taylor map
Strizhak-Kawcynski chaotic oscillator [117][118]	continuous	real	3	9
Symmetric Flow attractor [119]	continuous	real	3	1
Symplectic map
Tangent map
Thomas' cyclically symmetric attractor [120]	continuous	real	3	1
Tent map	discrete	real	1
Tinkerbell map	discrete	real	2	4
Triangle map
Ueda chaotic oscillator [121]	continuous	real	3	3
Van der Pol oscillator	continuous	real	1	3
Willamowski-Rössler model [122]	continuous	real	3	10
WINDMI chaotic attractor [123]	continuous	real	1	2
Zaslavskii map	discrete	real	2
Zaslavskii rotation map

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

1. Chaos from Euler Solution of ODEs
2. Chaos from Euler Solution of ODEs
3. On the dynamics of a new simple 2-D rational discrete mapping
4. Chaos from Euler Solution of ODEs
5. http://www.yangsky.us/ijcc/pdf/ijcc83/IJCC823.pdf
6. The Aizawa attractor
7. Local Stability and Hopf Bifurcation Analysis of the Arneodo’s System
8. Basin of attraction
9. 1981 The Burke & Shaw system
10. A new chaotic attractor coined
11. A new chaotic attractor coined
12. http://www.scholarpedia.org/article/Chua_circuit Chua Circuit
13. Clifford Attractors
14. Peter de Jong Attractors
15. A discrete population model of delayed regulation
16. Irregular Attractors
17. A New Finance Chaotic Attractor
18. Hyperchaos
19. Visions of Chaos 2D Strange Attractor Tutorial
20. A new chaotic system and beyond: The generalized Lorenz-like system
21. Gingerbreadman map
22. Mira Fractals
23. Half-inverted tearing
24. Halvorsen: A tribute to Dr. Edward Norton Lorenz
25. Peter de Jong Attractors
26. Hopalong orbit fractal
27. Irregular Attractors
28. Global chaos synchronization of hyperchaotic chen system by sliding model control
29. Hybrid chaos synchronization of hyperchaotic newton-leipnik systems by sliding mode control
30. Adaptive Synchronization for an Uncertain New Hyperchaotic Lorenz System
31. Hyper-Lu system
32. The first hyperchaotic system
33. Hyperchaotic attractor
34. Attractors
35. Knot fractal map
37. A new discrete chaotic map based on the composition of permutations
38. A 3D symmetrical toroidal chaos
39. Lozi maps
40. Moore-Spiegel Attractor
41. A new chaotic system and beyond: The generalized lorenz-like system
42. A New Chaotic Jerk Circuit
43. Adaptive control and synchronization of the Newton-Leipnik systems
44. Chaos Control and Hybrid Projective Synchronization of a Novel Chaotic System
45. Pickover
46. Polynomial Type-A
47. Polynomial Type-B
48. Polynomial Type-C
49. Quadrup Two Orbit Fractal
50. Rikitake chaotic attractor
51. Description of strange attractors using invariants of phase-plane
52. Skarya
53. Van der Pol Oscillator Equations
54. Shaw-Pol chaotic oscillator
55. The Shimiziu-Morioka System
56. Sprott B chaotic attractor
57. Chaos Blog - Sprott B system
58. Sprott C chaotic attractor
59. Chaos Blog - Sprott C system
60. Sprott's Gateway - Sprott-Linz A chaotic attractor
61. A new chaotic system and beyond: The generalized Lorenz-like System
62. Chaos Blog - Sprott-Linz A chaotic attractor
63. Sprott's Gateway - Sprott-Linz B chaotic attractor
64. A new chaotic system and beyond: The generalized Lorenz-like System
65. Chaos Blog - Sprott-Linz B chaotic attractor
66. Sprott's Gateway - Sprott-Linz C chaotic attractor
67. A new chaotic system and beyond: The generalized Lorenz-like System
68. Chaos Blog - Sprott-Linz C chaotic attractor
69. Sprott's Gateway - Sprott-Linz D chaotic attractor
70. A new chaotic system and beyond: The generalized Lorenz-like System
71. Chaos Blog - Sprott-Linz D chaotic attractor
72. Sprott's Gateway - Sprott-Linz E chaotic attractor
73. A new chaotic system and beyond: The generalized Lorenz-like System
74. Chaos Blog - Sprott-Linz E chaotic attractor
75. Sprott's Gateway - Sprott-Linz F chaotic attractor
76. A new chaotic system and beyond: The generalized Lorenz-like System
77. Chaos Blog - Sprott-Linz F chaotic attractor
78. Sprott's Gateway - Sprott-Linz G chaotic attractor
79. A new chaotic system and beyond: The generalized Lorenz-like System
80. Chaos Blog - Sprott-Linz G chaotic attractor
81. Sprott's Gateway - Sprott-Linz H chaotic attractor
82. A new chaotic system and beyond: The generalized Lorenz-like System
83. Chaos Blog - Sprott-Linz H chaotic attractor
84. Sprott's Gateway - Sprott-Linz I chaotic attractor
85. A new chaotic system and beyond: The generalized Lorenz-like System
86. Chaos Blog - Sprott-Linz I chaotic attractor
87. Sprott's Gateway - Sprott-Linz J chaotic attractor
88. A new chaotic system and beyond: The generalized Lorenz-like System
89. Chaos Blog - Sprott-Linz J chaotic attractor
90. Sprott's Gateway - Sprott-Linz K chaotic attractor
91. A new chaotic system and beyond: The generalized Lorenz-like System
92. Chaos Blog - Sprott-Linz K chaotic attractor
93. Sprott's Gateway - Sprott-Linz L chaotic attractor
94. A new chaotic system and beyond: The generalized Lorenz-like System
95. Chaos Blog - Sprott-Linz L chaotic attractor
96. Sprott's Gateway - Sprott-Linz M chaotic attractor
97. A new chaotic system and beyond: The generalized Lorenz-like System
98. Chaos Blog - Sprott-Linz M chaotic attractor
99. Sprott's Gateway - Sprott-Linz N chaotic attractor
100. A new chaotic system and beyond: The generalized Lorenz-like System
101. Chaos Blog - Sprott-Linz N chaotic attractor
102. Sprott's Gateway - Sprott-Linz O chaotic attractor
103. A new chaotic system and beyond: The generalized Lorenz-like System
104. Chaos Blog - Sprott-Linz O chaotic attractor
105. Sprott's Gateway - Sprott-Linz P chaotic attractor
106. A new chaotic system and beyond: The generalized Lorenz-like System
107. Chaos Blog - Sprott-Linz P chaotic attractor
108. Sprott's Gateway - Sprott-Linz Q chaotic attractor
109. A new chaotic system and beyond: The generalized Lorenz-like System
110. Chaos Blog - Sprott-Linz Q chaotic attractor
111. Sprott's Gateway - Sprott-Linz R chaotic attractor
112. A new chaotic system and beyond: The generalized Lorenz-like System
113. Chaos Blog - Sprott-Linz R chaotic attractor
114. Sprott's Gateway - Sprott-Linz S chaotic attractor
115. A new chaotic system and beyond: The generalized Lorenz-like System
116. Chaos Blog - Sprott-Linz S chaotic attractor
117. Strizhak-Kawcynski chaotic oscillator
118. Chaos Blog - Strizhak-Kawcynski chaotic oscillator
119. Sprott's Gateway - A symmetric chaotic flow
120. http://sprott.physics.wisc.edu/chaostsa/ Sprott's Gateway - Chaos and Time-Series Analysis
121. Oscillator of Ueda
122. Internal fluctuations in a model of chemical chaos