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List of chaotic maps

December 17, 2023

In mathematics, a chaotic map is a map (namely, 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 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 edit

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 system[citation needed] 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 - [1][2]
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 edit

See also: List of fractals by Hausdorff dimension

References edit

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  7. ^ Image encryption based on new Beta chaotic maps
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  12. ^ http://www.scholarpedia.org/article/Chua_circuit Chua Circuit
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  14. ^ Peter de Jong Attractors
  15. ^ A discrete population model of delayed regulation
  16. ^ Chaos from Euler Solution of ODEs
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  18. ^ Irregular Attractors
  19. ^ A New Finance Chaotic Attractor
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  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
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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
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  46. ^ Polynomial Type-B
  47. ^ Polynomial Type-C
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  51. ^ Skarya 2015-12-22 at the Wayback Machine
  52. ^ Van der Pol Oscillator Equations
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  68. ^ Sprott's Gateway - Sprott-Linz D chaotic attractor 2007-02-27 at the Wayback Machine
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  71. ^ Sprott's Gateway - Sprott-Linz E chaotic attractor 2007-02-27 at the Wayback Machine
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  74. ^ Sprott's Gateway - Sprott-Linz F chaotic attractor 2007-02-27 at the Wayback Machine
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  76. ^ Chaos Blog - Sprott-Linz F chaotic attractor 2015-12-22 at the Wayback Machine
  77. ^ Sprott's Gateway - Sprott-Linz G chaotic attractor 2007-02-27 at the Wayback Machine
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  79. ^ Chaos Blog - Sprott-Linz G chaotic attractor 2015-12-22 at the Wayback Machine
  80. ^ Sprott's Gateway - Sprott-Linz H chaotic attractor 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 2015-12-22 at the Wayback Machine
  83. ^ Sprott's Gateway - Sprott-Linz I chaotic attractor 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 2015-12-22 at the Wayback Machine
  86. ^ Sprott's Gateway - Sprott-Linz J chaotic attractor 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 2015-12-22 at the Wayback Machine
  89. ^ Sprott's Gateway - Sprott-Linz K chaotic attractor 2007-02-27 at the Wayback Machine
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  91. ^ Chaos Blog - Sprott-Linz K chaotic attractor 2015-12-22 at the Wayback Machine
  92. ^ Sprott's Gateway - Sprott-Linz L chaotic attractor 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 2015-12-22 at the Wayback Machine
  95. ^ Sprott's Gateway - Sprott-Linz M chaotic attractor 2007-02-27 at the Wayback Machine
  96. ^ A new chaotic system and beyond: The generalized Lorenz-like System
  97. ^ Chaos Blog - Sprott-Linz M chaotic attractor 2015-12-22 at the Wayback Machine
  98. ^ Sprott's Gateway - Sprott-Linz N chaotic attractor 2007-02-27 at the Wayback Machine
  99. ^ A new chaotic system and beyond: The generalized Lorenz-like System
  100. ^ Chaos Blog - Sprott-Linz N chaotic attractor 2015-12-22 at the Wayback Machine
  101. ^ Sprott's Gateway - Sprott-Linz O chaotic attractor 2007-02-27 at the Wayback Machine
  102. ^ A new chaotic system and beyond: The generalized Lorenz-like System
  103. ^ Chaos Blog - Sprott-Linz O chaotic attractor 2015-12-22 at the Wayback Machine
  104. ^ Sprott's Gateway - Sprott-Linz P chaotic attractor 2007-02-27 at the Wayback Machine
  105. ^ A new chaotic system and beyond: The generalized Lorenz-like System
  106. ^ Chaos Blog - Sprott-Linz P chaotic attractor 2015-12-22 at the Wayback Machine
  107. ^ Sprott's Gateway - Sprott-Linz Q chaotic attractor 2007-02-27 at the Wayback Machine
  108. ^ A new chaotic system and beyond: The generalized Lorenz-like System
  109. ^ Chaos Blog - Sprott-Linz Q chaotic attractor 2015-12-22 at the Wayback Machine
  110. ^ Sprott's Gateway - Sprott-Linz R chaotic attractor 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 2007-02-27 at the Wayback Machine
  114. ^ A new chaotic system and beyond: The generalized Lorenz-like System
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  118. ^ Sprott's Gateway - A symmetric chaotic flow
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  120. ^ Okulov, A. Yu.; Oraevsky, A. N. (1986). "Space–temporal behavior of a light pulse propagating in a nonlinear nondispersive medium". Journal of the Optical Society of America B. 3 (5): 741. doi:10.1364/JOSAB.3.000741. S2CID 124347430.
  121. ^ Okulov, A Yu; Oraevskiĭ, A. N. (1984). "Regular and stochastic self-modulation of radiation in a ring laser with a nonlinear element". Soviet Journal of Quantum Electronics. 14 (9): 1235–1237. doi:10.1070/QE1984v014n09ABEH006171.
  122. ^ Okulov, Alexey Yurievich (2020). "Numerical investigation of coherent and turbulent structures of light via nonlinear integral mappings". Computer Research and Modeling. 12 (5): 979–992. arXiv:1911.10694. doi:10.20537/2076-7633-2020-12-5-979-992. S2CID 211133329. {{cite journal}}: Check |url= value (help)
  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. ^ . 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. ^ Adaptive Backstepping Controller Design for the Anti-Synchronization of Identical WINDMI Chaotic Systems with Unknown Parameters and its SPICE Implementation
  129. ^ 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. S2CID 11406449.

December 17, 2023
list, chaotic, maps, mathematics, chaotic, namely, evolution, function, that, exhibits, some, sort, chaotic, behavior, maps, parameterized, discrete, time, continuous, time, parameter, discrete, maps, usually, take, form, iterated, functions, chaotic, maps, of. In mathematics a chaotic map is a map namely 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 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 editMap Time domain Space domain Number of space dimensions Number of parameters Also known as3 cells CNN system continuous real 32D Lorenz system 1 discrete real 2 1 Euler method approximation to non chaotic ODE 2D Rational chaotic map 2 discrete rational 2 2ACT chaotic attractor 3 continuous real 3Aizawa chaotic attractor 4 continuous real 3 5Arneodo chaotic system 5 continuous real 3Arnold s cat map discrete real 2 0Baker s map discrete real 2 0Basin chaotic map 6 discrete real 2 1Beta Chaotic Map 7 12Bogdanov map discrete real 2 3Brusselator continuous real 3Burke Shaw chaotic attractor 8 continuous real 3 2Chen 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 3Chossat Golubitsky symmetry mapChua circuit 12 continuous real 3 3Circle map discrete real 1 2Complex quadratic map discrete complex 1 1 gives rise to the Mandelbrot setComplex squaring map discrete complex 1 0 acts on the Julia set for the squaring map Complex cubic map discrete complex 1 2Clifford fractal map 13 discrete real 2 4Degenerate Double Rotor mapDe Jong fractal map 14 discrete real 2 4Delayed Logistic system 15 discrete real 2 1Discretized 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 mapDuffing map discrete real 2 2 Holmes chaotic mapDuffing equation continuous real 2 5 3 independent Dyadic transformation discrete real 1 0 2x mod 1 map Bernoulli map doubling map sawtooth mapExponential map discrete complex 2 1Feigenbaum strange nonchaotic map 18 discrete real 3Finance system 19 continuous real 3Folded Towel hyperchaotic map 20 continuous real 3Fractal Dream system 21 discrete real 2Gauss map discrete real 1 mouse map Gaussian mapGeneralized Baker mapGenesio Tesi chaotic attractor 22 continuous real 3Gingerbreadman map 23 discrete real 2 0Grinch dragon fractal discrete real 2Gumowski Mira map 24 discrete real 2 1Hadley chaotic circulation continuous real 3 0Half inverted Rossler attractor 25 Halvorsen chaotic attractor 26 continuous real 3Henon map discrete real 2 2Henon with 5th order polynomialHindmarsh Rose neuronal model continuous real 3 8Hitzl Zele mapHorseshoe map discrete real 2 1Hopa Jong fractal 27 discrete real 2Hopalong orbit fractal 28 discrete real 2Hyper Logistic map 29 discrete real 2Hyperchaotic Chen system 30 continuous real 3Hyper Newton Leipnik system citation needed continuous real 4Hyper Lorenz chaotic attractor continuous real 4Hyper Lu chaotic system 31 continuous real 4Hyper Rossler chaotic attractor 32 continuous real 4Hyperchaotic attractor 33 continuous real 4Ikeda chaotic attractor 34 continuous real 3Ikeda map discrete real 2 3 Ikeda fractal mapInterval exchange map discrete real 1 variableKaplan Yorke map discrete real 2 1Knot fractal map 35 discrete real 2Knot Holder chaotic oscillator 36 continuous real 3Kuramoto Sivashinsky equation continuous realLambic map 37 discrete discrete 1Li symmetrical toroidal chaos 38 continuous real 3Linear map on unit squareLogistic map discrete real 1 1Lorenz system continuous real 3 3Lorenz system s Poincare return map discrete real 2 3Lorenz 96 model continuous real arbitrary 1Lotka Volterra system continuous real 3 9Lozi map 39 discrete real 2Moore Spiegel chaotic oscillator 40 continuous real 3Scroll Attractor 41 continuous real 3Jerk Circuit 42 continuous real 3Newton Leipnik system continuous real 3Nordmark truncated mapNose Hoover system continuous real 3Novel chaotic system 43 continuous real 3Pickover fractal map 44 continuous real 3Pomeau 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 3Polynom Type B fractal map 46 continuous real 3 6Polynom Type C fractal map 47 continuous real 3 18Pulsed rotorQuadrup Two orbit fractal 48 discrete real 2 3Quasiperiodicity mapMikhail Anatoly chaotic attractor continuous real 3 2Random Rotate mapRayleigh Benard chaotic oscillator continuous real 3 3Rikitake chaotic attractor 49 continuous real 3 3Rossler attractor continuous real 3 3Rucklidge system 50 continuous real 3 2Sakarya chaotic attractor 51 continuous real 3 2Shaw Pol chaotic oscillator 52 53 continuous real 3 3Shimizu Morioka system 54 continuous real 3 2Shobu Ose Mori piecewise linear map discrete real 1 piecewise linear approximation for Pomeau Manneville Type I mapSinai map 1 2 Sprott B chaotic system 55 56 continuous real 3 2Sprott C chaotic system 57 58 continuous real 3 3Sprott Linz A chaotic attractor 59 60 61 continuous real 3 0Sprott Linz B chaotic attractor 62 63 64 continuous real 3 0Sprott Linz C chaotic attractor 65 66 67 continuous real 3 0Sprott Linz D chaotic attractor 68 69 70 continuous real 3 1Sprott Linz E chaotic attractor 71 72 73 continuous real 3 1Sprott Linz F chaotic attractor 74 75 76 continuous real 3 1Sprott Linz G chaotic attractor 77 78 79 continuous real 3 1Sprott Linz H chaotic attractor 80 81 82 continuous real 3 1Sprott Linz I chaotic attractor 83 84 85 continuous real 3 1Sprott Linz J chaotic attractor 86 87 88 continuous real 3 1Sprott Linz K chaotic attractor 89 90 91 continuous real 3 1Sprott Linz L chaotic attractor 92 93 94 continuous real 3 2Sprott Linz M chaotic attractor 95 96 97 continuous real 3 1Sprott Linz N chaotic attractor 98 99 100 continuous real 3 1Sprott Linz O chaotic attractor 101 102 103 continuous real 3 1Sprott Linz P chaotic attractor 104 105 106 continuous real 3 1Sprott Linz Q chaotic attractor 107 108 109 continuous real 3 2Sprott Linz R chaotic attractor 110 111 112 continuous real 3 2Sprott Linz S chaotic attractor 113 114 115 continuous real 3 1Standard map Kicked rotor discrete real 2 1 Chirikov standard map Chirikov Taylor mapStrizhak Kawczynski chaotic oscillator 116 117 continuous real 3 9Symmetric Flow attractor 118 continuous real 3 1Symplectic mapTangent mapTahn map 119 discrete real 1 1 Ring laser map 120 Beta distribution 121 122 Thomas cyclically symmetric attractor 123 continuous real 3 1Tent map discrete real 1Tinkerbell map discrete real 2 4Triangle mapUeda chaotic oscillator 124 continuous real 3 3Van der Pol oscillator continuous real 2 3Willamowski Rossler model 125 continuous real 3 10WINDMI chaotic attractor 126 127 128 continuous real 1 2Zaslavskii map discrete real 2 4Zaslavskii rotation mapZeraoulia Sprott map 129 discrete real 2 2Chialvo map discrete discrete 3List of fractals editSee also List of fractals by Hausdorff dimension 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 triangleReferences edit Chaos from Euler Solution of ODEs On the dynamics of a new simple 2 D rational discrete mapping http www yangsky us ijcc pdf ijcc83 IJCC823 pdf permanent dead link 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 amp Shaw system A new chaotic attractor coined 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 Chaos from Euler Solution of ODEs Chaos from Euler Solution of ODEs 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 Lefranc Marc Letellier Christophe Gilmore Robert 2008 Chaos topology Scholarpedia 3 7 4592 Bibcode 2008SchpJ 3 4592G doi 10 4249 scholarpedia 4592 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 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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 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investigation of coherent and turbulent structures of light via nonlinear integral mappings Computer Research and Modeling 12 5 979 992 arXiv 1911 10694 doi 10 20537 2076 7633 2020 12 5 979 992 S2CID 211133329 a href Template Cite journal html title Template Cite journal cite journal a Check url value help 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 Main Page Weigel s Research and Teaching Page aurora gmu edu Archived from the original on 10 April 2011 Retrieved 17 January 2022 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 S2CID 11406449 Retrieved from https en wikipedia org w index php title List of chaotic maps amp oldid 1170156184, wikipedia, wiki, book, books, library,

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