List of chaotic maps

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search

Template:Short description

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.

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

Map Time domain Space domain Number of space dimensions Number of parameters Also known as
3-cells CNN system continuous real 3
2D Lorenz system[1] discrete real 2 1 Euler method approximation to (non-chaotic) ODE.
2D Rational chaotic map[2] discrete rational 2 2
ACT chaotic attractor [3] continuous real 3
Aizawa chaotic attractor[4] continuous real 3 5
Arneodo chaotic system[5] continuous real 3
Arnold's cat map discrete real 2 0
Baker's map discrete real 2 0
Basin chaotic map[6] discrete real 2 1
Beta Chaotic Map[7] 12
Bogdanov map discrete real 2 3
Brusselator continuous real 3
Burke-Shaw chaotic attractor[8] continuous real 3 2
Chen chaotic attractor[9] continuous real 3 3 Not topologically conjugate to the Lorenz attractor.
Chen-Celikovsky system[10] continuous real 3 "Generalized Lorenz canonical form of chaotic systems"
Chen-LU system[11] continuous real 3 3 Interpolates between Lorenz-like and Chen-like behavior.
Chen-Lee system continuous real 3
Chossat-Golubitsky symmetry map
Chua circuit[12] 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[13] discrete real 2 4
Degenerate Double Rotor map
De Jong fractal map[14] discrete real 2 4
Delayed-Logistic system[15] discrete real 2 1
Discretized circular Van der Pol system[16] discrete real 2 1 Euler method approximation to 'circular' Van der Pol-like ODE.
Discretized Van der Pol system[17] discrete real 2 2 Euler method approximation to Van der Pol ODE.
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[18] discrete real 3
Finance system[19] continuous real 3
Folded-Towel hyperchaotic map[20] continuous real 3
Fractal-Dream system[21] discrete real 2
Gauss map discrete real 1 mouse map, Gaussian map
Generalized Baker map
Genesio-Tesi chaotic attractor[22] continuous real 3
Gingerbreadman map[23] discrete real 2 0
Grinch dragon fractal discrete real 2
Gumowski/Mira map[24] discrete real 2 1
Hadley chaotic circulation continuous real 3 0
Half-inverted Rössler attractor[25]
Halvorsen chaotic attractor[26] 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[27] discrete real 2
Hopalong orbit fractal[28] discrete real 2
Hyper Logistic map[29] discrete real 2
Hyperchaotic Chen system[30] continuous real 3
Hyper Newton-Leipnik systemScript error: No such module "Unsubst". continuous real 4
Hyper-Lorenz chaotic attractor 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 3 Ikeda fractal map
Interval exchange map discrete real 1 variable
Kaplan-Yorke map discrete real 2 1
Knot fractal map[35] discrete real 2
Knot-Holder chaotic oscillator[36] continuous real 3
Kuramoto–Sivashinsky equation continuous real
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 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 9
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 continuous real 3
Nordmark truncated map
Nosé-Hoover system continuous real 3
Novel chaotic system[43] continuous real 3
Pickover fractal map[44] 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[45] continuous real 3 3
Polynom Type-B fractal map[46] continuous real 3 6
Polynom Type-C fractal map[47] continuous real 3 18
Pulsed rotor
Quadrup-Two orbit fractal[48] 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[49] continuous real 3 3
Rössler attractor continuous real 3 3
Rucklidge system[50] continuous real 3 2
Sakarya chaotic attractor[51] continuous real 3 2
Shaw-Pol chaotic oscillator[52][53] continuous real 3 3
Shimizu-Morioka system[54] continuous real 3 2
Shobu-Ose-Mori piecewise-linear map discrete real 1 piecewise-linear approximation for Pomeau-Manneville Type I map
Sinai map - [2][3]
Sprott B chaotic system[55][56] continuous real 3 2
Sprott C chaotic system[57][58] continuous real 3 3
Sprott-Linz A chaotic attractor[59][60][61] continuous real 3 0
Sprott-Linz B chaotic attractor[62][63][64] continuous real 3 0
Sprott-Linz C chaotic attractor[65][66][67] continuous real 3 0
Sprott-Linz D chaotic attractor[68][69][70] continuous real 3 1
Sprott-Linz E chaotic attractor[71][72][73] continuous real 3 1
Sprott-Linz F chaotic attractor[74][75][76] continuous real 3 1
Sprott-Linz G chaotic attractor[77][78][79] continuous real 3 1
Sprott-Linz H chaotic attractor[80][81][82] continuous real 3 1
Sprott-Linz I chaotic attractor[83][84][85] continuous real 3 1
Sprott-Linz J chaotic attractor[86][87][88] continuous real 3 1
Sprott-Linz K chaotic attractor[89][90][91] continuous real 3 1
Sprott-Linz L chaotic attractor[92][93][94] continuous real 3 2
Sprott-Linz M chaotic attractor[95][96][97] continuous real 3 1
Sprott-Linz N chaotic attractor[98][99][100] continuous real 3 1
Sprott-Linz O chaotic attractor[101][102][103] continuous real 3 1
Sprott-Linz P chaotic attractor[104][105][106] continuous real 3 1
Sprott-Linz Q chaotic attractor[107][108][109] continuous real 3 2
Sprott-Linz R chaotic attractor[110][111][112] continuous real 3 2
Sprott-Linz S chaotic attractor[113][114][115] continuous real 3 1
Standard map, Kicked rotor discrete real 2 1 Chirikov standard map, Chirikov-Taylor map
Strizhak-Kawczynski chaotic oscillator[116][117] continuous real 3 9
Symmetric Flow attractor[118] continuous real 3 1
Symplectic map
Tangent map
Tahn map[119] discrete real 1 1 Ring laser map [120]Beta distribution[121]

[122]

Thomas' cyclically symmetric attractor[123] continuous real 3 1
Tent map discrete real 1
Tinkerbell map discrete real 2 4
Triangle map
Ueda chaotic oscillator[124] continuous real 3 3
Van der Pol oscillator continuous real 2 3
Willamowski-Rössler model[125] continuous real 3 10
WINDMI chaotic attractor[126][127][128] continuous real 1 2
Zaslavskii map discrete real 2 4
Zaslavskii rotation map
Zeraoulia-Sprott map[129] discrete real 2 2
Chialvo map discrete discrete 3

List of fractals

Script error: No such module "Labelled list hatnote".

References

<templatestyles src="Reflist/styles.css" />

  1. ↑ Chaos from Euler Solution of ODEs
  2. ↑ On the dynamics of a new simple 2-D rational discrete mapping
  3. ↑ [1]Template:Category handler[<span title="Script error: No such module "string".">usurped]Script error: No such module "Check for unknown parameters".
  4. ↑ The Aizawa attractor
  5. ↑ Local Stability and Hopf Bifurcation Analysis of the Arneodo’s System
  6. ↑ Basin of attraction Script error: No such module "webarchive".
  7. ↑ Script error: No such module "Citation/CS1".
  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 Script error: No such module "webarchive".
  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 controlTemplate:Category handler[<span title="Script error: No such module "string".">usurped]Script error: No such module "Check for unknown parameters".
  31. ↑ Hyper-Lu system
  32. ↑ The first hyperchaotic system
  33. ↑ Hyperchaotic attractor Script error: No such module "webarchive".
  34. ↑ Attractors
  35. ↑ Knot fractal map Script error: No such module "webarchive".
  36. ↑ Script error: No such module "Citation/CS1".
  37. ↑ Script error: No such module "Citation/CS1".
  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 Script error: No such module "webarchive".
  50. ↑ Description of strange attractors using invariants of phase-plane
  51. ↑ Skarya Script error: No such module "webarchive".
  52. ↑ Van der Pol Oscillator Equations
  53. ↑ Shaw-Pol chaotic oscillator Script error: No such module "webarchive".
  54. ↑ The Shimiziu-Morioka System
  55. ↑ Sprott B chaotic attractor Script error: No such module "webarchive".
  56. ↑ Chaos Blog - Sprott B system Script error: No such module "webarchive".
  57. ↑ Sprott C chaotic attractor Script error: No such module "webarchive".
  58. ↑ Chaos Blog - Sprott C system Script error: No such module "webarchive".
  59. ↑ Sprott's Gateway - Sprott-Linz A chaotic attractor Script error: No such module "webarchive".
  60. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  61. ↑ Chaos Blog - Sprott-Linz A chaotic attractor Script error: No such module "webarchive".
  62. ↑ Sprott's Gateway - Sprott-Linz B chaotic attractor Script error: No such module "webarchive".
  63. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  64. ↑ Chaos Blog - Sprott-Linz B chaotic attractor Script error: No such module "webarchive".
  65. ↑ Sprott's Gateway - Sprott-Linz C chaotic attractor Script error: No such module "webarchive".
  66. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  67. ↑ Chaos Blog - Sprott-Linz C chaotic attractor Script error: No such module "webarchive".
  68. ↑ Sprott's Gateway - Sprott-Linz D chaotic attractor Script error: No such module "webarchive".
  69. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  70. ↑ Chaos Blog - Sprott-Linz D chaotic attractor Script error: No such module "webarchive".
  71. ↑ Sprott's Gateway - Sprott-Linz E chaotic attractor Script error: No such module "webarchive".
  72. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  73. ↑ Chaos Blog - Sprott-Linz E chaotic attractor Script error: No such module "webarchive".
  74. ↑ Sprott's Gateway - Sprott-Linz F chaotic attractor Script error: No such module "webarchive".
  75. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  76. ↑ Chaos Blog - Sprott-Linz F chaotic attractor Script error: No such module "webarchive".
  77. ↑ Sprott's Gateway - Sprott-Linz G chaotic attractor Script error: No such module "webarchive".
  78. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  79. ↑ Chaos Blog - Sprott-Linz G chaotic attractor Script error: No such module "webarchive".
  80. ↑ Sprott's Gateway - Sprott-Linz H chaotic attractor Script error: No such module "webarchive".
  81. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  82. ↑ Chaos Blog - Sprott-Linz H chaotic attractor Script error: No such module "webarchive".
  83. ↑ Sprott's Gateway - Sprott-Linz I chaotic attractor Script error: No such module "webarchive".
  84. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  85. ↑ Chaos Blog - Sprott-Linz I chaotic attractor Script error: No such module "webarchive".
  86. ↑ Sprott's Gateway - Sprott-Linz J chaotic attractor Script error: No such module "webarchive".
  87. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  88. ↑ Chaos Blog - Sprott-Linz J chaotic attractor Script error: No such module "webarchive".
  89. ↑ Sprott's Gateway - Sprott-Linz K chaotic attractor Script error: No such module "webarchive".
  90. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  91. ↑ Chaos Blog - Sprott-Linz K chaotic attractor Script error: No such module "webarchive".
  92. ↑ Sprott's Gateway - Sprott-Linz L chaotic attractor Script error: No such module "webarchive".
  93. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  94. ↑ Chaos Blog - Sprott-Linz L chaotic attractor Script error: No such module "webarchive".
  95. ↑ Sprott's Gateway - Sprott-Linz M chaotic attractor Script error: No such module "webarchive".
  96. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  97. ↑ Chaos Blog - Sprott-Linz M chaotic attractor Script error: No such module "webarchive".
  98. ↑ Sprott's Gateway - Sprott-Linz N chaotic attractor Script error: No such module "webarchive".
  99. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  100. ↑ Chaos Blog - Sprott-Linz N chaotic attractor Script error: No such module "webarchive".
  101. ↑ Sprott's Gateway - Sprott-Linz O chaotic attractor Script error: No such module "webarchive".
  102. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  103. ↑ Chaos Blog - Sprott-Linz O chaotic attractor Script error: No such module "webarchive".
  104. ↑ Sprott's Gateway - Sprott-Linz P chaotic attractor Script error: No such module "webarchive".
  105. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  106. ↑ Chaos Blog - Sprott-Linz P chaotic attractor Script error: No such module "webarchive".
  107. ↑ Sprott's Gateway - Sprott-Linz Q chaotic attractor Script error: No such module "webarchive".
  108. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  109. ↑ Chaos Blog - Sprott-Linz Q chaotic attractor Script error: No such module "webarchive".
  110. ↑ Sprott's Gateway - Sprott-Linz R chaotic attractor Script error: No such module "webarchive".
  111. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  112. ↑ Chaos Blog - Sprott-Linz R chaotic attractor Script error: No such module "webarchive".
  113. ↑ Sprott's Gateway - Sprott-Linz S chaotic attractor Script error: No such module "webarchive".
  114. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
  115. ↑ Chaos Blog - Sprott-Linz S chaotic attractor Script error: No such module "webarchive".
  116. ↑ Strizhak-Kawczynski chaotic oscillatorScript error: No such module "Unsubst".
  117. ↑ Chaos Blog - Strizhak-Kawczynski chaotic oscillator Script error: No such module "webarchive".
  118. ↑ Sprott's Gateway - A symmetric chaotic flow
  119. ↑ Script error: No such module "Citation/CS1".Script error: No such module "Unsubst".
  120. ↑ Script error: No such module "Citation/CS1".
  121. ↑ Script error: No such module "Citation/CS1".
  122. ↑ Script error: No such module "Citation/CS1".Script error: No such module "Unsubst".
  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. ↑ Script error: No such module "citation/CS1".
  127. ↑ Synchronization of Chaotic Fractional-Order WINDMI Systems via Linear State Error Feedback Control
  128. ↑ Script error: No such module "Citation/CS1".
  129. ↑ Script error: No such module "Citation/CS1".

Script error: No such module "Check for unknown parameters".

Template:Chaos theory

Retrieved from "http://debianws.lexgopc.com/wiki143/index.php?title=List_of_chaotic_maps&oldid=1487966"