List of chaotic maps

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In mathematics, a chaotic map is a map (an 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.

Contents

Chaotic maps and iterated functions often generate fractals. Some fractals are studied as objects themselves, as sets rather than in terms of the maps that generate them. This is often because there are several different iterative procedures that generate the same fractal. See also Universality (dynamical systems).

List of chaotic maps

MapTime domainSpace domainNumber of space dimensionsNumber of parametersAlso known as
3-cells CNN system continuousreal3
2D Lorenz system [1] discretereal21 Euler method approximation to (non-chaotic) ODE.
2D Rational chaotic map [2] discreterational22
ACT chaotic attractor [3] continuousreal3
Aizawa chaotic attractor [4] continuousreal35
Arneodo chaotic system [5] continuousreal3
Arnold's cat map discretereal20
Baker's map discretereal20
Basin chaotic map [6] discretereal21
Beta Chaotic Map [7] 12
Bogdanov map discretereal23
Brusselator continuousreal3
Burke-Shaw chaotic attractor [8] continuousreal32
Chen chaotic attractor [9] continuousreal33Not topologically conjugate to the Lorenz attractor.
Chen-Celikovsky system [10] continuousreal3"Generalized Lorenz canonical form of chaotic systems"
Chen-LU system [11] continuousreal33Interpolates between Lorenz-like and Chen-like behavior.
Chen-Lee system continuousreal3
Chossat-Golubitsky symmetry map
Chua circuit [12] continuousreal33
Circle map discretereal12
Complex quadratic map discretecomplex11gives rise to the Mandelbrot set
Complex squaring map discretecomplex10acts on the Julia set for the squaring map.
Complex cubic map discretecomplex12
Clifford fractal map [13] discretereal24
Degenerate Double Rotor map
De Jong fractal map [14] discretereal24
Delayed-Logistic system [15] discretereal21
Discretized circular Van der Pol system [16] discretereal21 Euler method approximation to 'circular' Van der Pol-like ODE.
Discretized Van der Pol system [17] discretereal22 Euler method approximation to Van der Pol ODE.
Double rotor map
Duffing map discretereal22Holmes chaotic map
Duffing equation continuousreal25 (3 independent)
Dyadic transformation discretereal102x mod 1 map, Bernoulli map, doubling map, sawtooth map
Exponential map discretecomplex21
Feigenbaum strange nonchaotic map [18] discretereal3
Finance system [19] continuousreal3
Folded-Towel hyperchaotic map [20] continuousreal3
Fractal-Dream system [21] discretereal2
Gauss map discretereal1mouse map, Gaussian map
Generalized Baker map
Genesio-Tesi chaotic attractor [22] continuousreal3
Gingerbreadman map [23] discretereal20
Grinch dragon fractal discretereal2
Gumowski/Mira map [24] discretereal21
Hadley chaotic circulation continuousreal30
Half-inverted Rössler attractor [25]
Halvorsen chaotic attractor [26] continuousreal3
Hénon map discretereal22
Hénon with 5th order polynomial
Hindmarsh-Rose neuronal model continuousreal38
Hitzl-Zele map
Horseshoe map discretereal21
Hopa-Jong fractal [27] discretereal2
Hopalong orbit fractal [28] discretereal2
Hyper Logistic map [29] discretereal2
Hyperchaotic Chen system [30] continuousreal3
Hyper Newton-Leipnik system [ citation needed ]continuousreal4
Hyper-Lorenz chaotic attractor continuousreal4
Hyper-Lu chaotic system [31] continuousreal4
Hyper-Rössler chaotic attractor [32] continuousreal4
Hyperchaotic attractor [33] continuousreal4
Ikeda chaotic attractor [34] continuousreal3
Ikeda map discretereal23Ikeda fractal map
Interval exchange map discretereal1variable
Kaplan-Yorke map discretereal21
Knot fractal map [35] discretereal2
Knot-Holder chaotic oscillator [36] continuousreal3
Kuramoto–Sivashinsky equation continuousreal
Lambić map [37] discretediscrete1
Li symmetrical toroidal chaos [38] continuousreal3
Linear map on unit square
Logistic map discretereal11
Lorenz system continuousreal33
Lorenz system's Poincaré return map discretereal23
Lorenz 96 model continuousrealarbitrary1
Lotka-Volterra system continuousreal39
Lozi map [39] discretereal2
Moore-Spiegel chaotic oscillator [40] continuousreal3
Scroll-Attractor [41] continuousreal3
Jerk Circuit [42] continuousreal3
Newton-Leipnik system continuousreal3
Nordmark truncated map
Nosé-Hoover system continuousreal3
Novel chaotic system [43] continuousreal3
Pickover fractal map [44] continuousreal3
Pomeau-Manneville maps for intermittent chaos discretereal1 or 2Normal-form maps for intermittency (Types I, II and III)
Polynom Type-A fractal map [45] continuousreal33
Polynom Type-B fractal map [46] continuousreal36
Polynom Type-C fractal map [47] continuousreal318
Pulsed rotor
Quadrup-Two orbit fractal [48] discretereal23
Quasiperiodicity map
Mikhail Anatoly chaotic attractor continuousreal32
Random Rotate map
Rayleigh-Benard chaotic oscillator continuousreal33
Rikitake chaotic attractor [49] continuousreal33
Rössler attractor continuousreal33
Rucklidge system [50] continuousreal32
Sakarya chaotic attractor [51] continuousreal32
Shaw-Pol chaotic oscillator [52] [53] continuousreal33
Shimizu-Morioka system [54] continuousreal32
Shobu-Ose-Mori piecewise-linear map discretereal1piecewise-linear approximation for Pomeau-Manneville Type I map
Sinai map -
Sprott B chaotic system [55] [56] continuousreal32
Sprott C chaotic system [57] [58] continuousreal33
Sprott-Linz A chaotic attractor [59] [60] [61] continuousreal30
Sprott-Linz B chaotic attractor [62] [63] [64] continuousreal30
Sprott-Linz C chaotic attractor [65] [66] [67] continuousreal30
Sprott-Linz D chaotic attractor [68] [69] [70] continuousreal31
Sprott-Linz E chaotic attractor [71] [72] [73] continuousreal31
Sprott-Linz F chaotic attractor [74] [75] [76] continuousreal31
Sprott-Linz G chaotic attractor [77] [78] [79] continuousreal31
Sprott-Linz H chaotic attractor [80] [81] [82] continuousreal31
Sprott-Linz I chaotic attractor [83] [84] [85] continuousreal31
Sprott-Linz J chaotic attractor [86] [87] [88] continuousreal31
Sprott-Linz K chaotic attractor [89] [90] [91] continuousreal31
Sprott-Linz L chaotic attractor [92] [93] [94] continuousreal32
Sprott-Linz M chaotic attractor [95] [96] [97] continuousreal31
Sprott-Linz N chaotic attractor [98] [99] [100] continuousreal31
Sprott-Linz O chaotic attractor [101] [102] [103] continuousreal31
Sprott-Linz P chaotic attractor [104] [105] [106] continuousreal31
Sprott-Linz Q chaotic attractor [107] [108] [109] continuousreal32
Sprott-Linz R chaotic attractor [110] [111] [112] continuousreal32
Sprott-Linz S chaotic attractor [113] [114] [115] continuousreal31
Standard map, Kicked rotor discretereal21Chirikov standard map, Chirikov-Taylor map
Strizhak-Kawczynski chaotic oscillator [116] [117] continuousreal39
Symmetric Flow attractor [118] continuousreal31
Symplectic map
Tangent map
Tahn map [119] discretereal11Ring laser map [120] Beta distribution [121]

[122]

Thomas' cyclically symmetric attractor [123] continuousreal31
Tent map discretereal1
Tinkerbell map discretereal24
Triangle map
Ueda chaotic oscillator [124] continuousreal33
Van der Pol oscillator continuousreal23
Willamowski-Rössler model [125] continuousreal310
WINDMI chaotic attractor [126] [127] [128] continuousreal12
Zaslavskii map discretereal24
Zaslavskii rotation map
Zeraoulia-Sprott map [129] discretereal22
Chialvo map discretediscrete3

List of fractals

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References

  1. ↑ Chaos from Euler Solution of ODEs
  2. ↑ On the dynamics of a new simple 2-D rational discrete mapping
  3. ↑ http://www.yangsky.us/ijcc/pdf/ijcc83/IJCC823.pdf%5B%5D
  4. ↑ The Aizawa attractor
  5. ↑ Local Stability and Hopf Bifurcation Analysis of the Arneodo’s System
  6. ↑ Basin of attraction Archived 2014-07-01 at the Wayback Machine
  7. ↑ Zahmoul, Rim; Ejbali, Ridha; Zaied, Mourad (2017). "Image encryption based on new Beta chaotic maps". Optics and Lasers in Engineering. 96: 39–49. Bibcode:2017OptLE..96...39Z. doi:10.1016/j.optlaseng.2017.04.009.
  8. ↑ 1981 The Burke & Shaw system
  9. ↑ A new chaotic attractor coined
  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. ↑ Chaos from Euler Solution of ODEs
  17. ↑ Chaos from Euler Solution of ODEs
  18. ↑ Irregular Attractors
  19. ↑ A New Finance Chaotic Attractor
  20. ↑ Hyperchaos Archived 2015-12-22 at the Wayback Machine
  21. ↑ Visions of Chaos 2D Strange Attractor Tutorial
  22. ↑ A new chaotic system and beyond: The generalized Lorenz-like system
  23. ↑ Gingerbreadman map
  24. ↑ Mira Fractals
  25. ↑ Half-inverted tearing
  26. ↑ Halvorsen: A tribute to Dr. Edward Norton Lorenz
  27. ↑ Peter de Jong Attractors
  28. ↑ Hopalong orbit fractal
  29. ↑ Irregular Attractors
  30. ↑ Global chaos synchronization of hyperchaotic chen system by sliding model control
  31. ↑ Hyper-Lu system
  32. ↑ The first hyperchaotic system
  33. ↑ Hyperchaotic attractor Archived 2015-12-22 at the Wayback Machine
  34. ↑ Attractors
  35. ↑ Knot fractal map Archived 2015-12-22 at the Wayback Machine
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  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. ↑ Chaos Control and Hybrid Projective Synchronization of a Novel Chaotic System
  44. ↑ Pickover
  45. ↑ Polynomial Type-A
  46. ↑ Polynomial Type-B
  47. ↑ Polynomial Type-C
  48. ↑ Quadrup Two Orbit Fractal
  49. ↑ Rikitake chaotic attractor Archived 2010-06-20 at the Wayback Machine
  50. ↑ Description of strange attractors using invariants of phase-plane
  51. ↑ Skarya Archived 2015-12-22 at the Wayback Machine
  52. ↑ Van der Pol Oscillator Equations
  53. ↑ Shaw-Pol chaotic oscillator Archived 2015-12-22 at the Wayback Machine
  54. ↑ The Shimiziu-Morioka System
  55. ↑ Sprott B chaotic attractor Archived 2007-02-27 at the Wayback Machine
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  57. ↑ Sprott C chaotic attractor Archived 2007-02-27 at the Wayback Machine
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  71. ↑ Sprott's Gateway - Sprott-Linz E chaotic attractor Archived 2007-02-27 at the Wayback Machine
  72. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  73. ↑ Chaos Blog - Sprott-Linz E chaotic attractor Archived 2015-12-22 at the Wayback Machine
  74. ↑ Sprott's Gateway - Sprott-Linz F chaotic attractor Archived 2007-02-27 at the Wayback Machine
  75. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  76. ↑ Chaos Blog - Sprott-Linz F chaotic attractor Archived 2015-12-22 at the Wayback Machine
  77. ↑ Sprott's Gateway - Sprott-Linz G chaotic attractor Archived 2007-02-27 at the Wayback Machine
  78. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  79. ↑ Chaos Blog - Sprott-Linz G chaotic attractor Archived 2015-12-22 at the Wayback Machine
  80. ↑ Sprott's Gateway - Sprott-Linz H chaotic attractor Archived 2007-02-27 at the Wayback Machine
  81. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  82. ↑ Chaos Blog - Sprott-Linz H chaotic attractor Archived 2015-12-22 at the Wayback Machine
  83. ↑ Sprott's Gateway - Sprott-Linz I chaotic attractor Archived 2007-02-27 at the Wayback Machine
  84. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  85. ↑ Chaos Blog - Sprott-Linz I chaotic attractor Archived 2015-12-22 at the Wayback Machine
  86. ↑ Sprott's Gateway - Sprott-Linz J chaotic attractor Archived 2007-02-27 at the Wayback Machine
  87. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  88. ↑ Chaos Blog - Sprott-Linz J chaotic attractor Archived 2015-12-22 at the Wayback Machine
  89. ↑ Sprott's Gateway - Sprott-Linz K chaotic attractor Archived 2007-02-27 at the Wayback Machine
  90. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
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  92. ↑ Sprott's Gateway - Sprott-Linz L chaotic attractor Archived 2007-02-27 at the Wayback Machine
  93. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  94. ↑ Chaos Blog - Sprott-Linz L chaotic attractor Archived 2015-12-22 at the Wayback Machine
  95. ↑ Sprott's Gateway - Sprott-Linz M chaotic attractor Archived 2007-02-27 at the Wayback Machine
  96. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
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  98. ↑ Sprott's Gateway - Sprott-Linz N chaotic attractor Archived 2007-02-27 at the Wayback Machine
  99. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
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  101. ↑ Sprott's Gateway - Sprott-Linz O chaotic attractor Archived 2007-02-27 at the Wayback Machine
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  104. ↑ Sprott's Gateway - Sprott-Linz P chaotic attractor Archived 2007-02-27 at the Wayback Machine
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  110. ↑ Sprott's Gateway - Sprott-Linz R chaotic attractor Archived 2007-02-27 at the Wayback Machine
  111. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
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  113. ↑ Sprott's Gateway - Sprott-Linz S chaotic attractor Archived 2007-02-27 at the Wayback Machine
  114. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  115. ↑ Chaos Blog - Sprott-Linz S chaotic attractor Archived 2015-12-22 at the Wayback Machine
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  117. ↑ Chaos Blog - Strizhak-Kawczynski chaotic oscillator Archived 2015-12-22 at the Wayback Machine
  118. ↑ Sprott's Gateway - A symmetric chaotic flow
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  123. ↑ http://sprott.physics.wisc.edu/chaostsa/ Sprott's Gateway - Chaos and Time-Series Analysis
  124. ↑ Oscillator of Ueda
  125. ↑ Internal fluctuations in a model of chemical chaos
  126. ↑ "Main Page - Weigel's Research and Teaching Page". aurora.gmu.edu. Archived from the original on 10 April 2011. Retrieved 17 January 2022.
  127. ↑ Synchronization of Chaotic Fractional-Order WINDMI Systems via Linear State Error Feedback Control
  128. ↑ Vaidyanathan, S.; Volos, Ch. K.; Rajagopal, K.; Kyprianidis, I. M.; Stouboulos, I. N. (2015). "Adaptive Backstepping Controller Design for the Anti-Synchronization of Identical WINDMI Chaotic Systems with Unknown Parameters and its SPICE Implementation" (PDF). Journal of Engineering Science and Technology Review. 8 (2): 74–82. doi:10.25103/jestr.082.11.
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