Ағылшыншамен салыстырыңыз: абзацты басыңыз — түпнұсқа терезеде ашылады. Абзац астындағы EN түймесі оны мәтін ішінде көрсетеді.
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Математикада хаотикалық карта – қандай да бір хаотикалық әрекеттерді көрсететін карта (эволюциялық функция). Карталар дискретті немесе үздіксіз уақыт параметрлерімен сипатталуы мүмкін. Дискретті карталар көбінесе итерацияланған функциялар түрінде болады. Хаотикалық карталар динамикалық жүйелерді зерттеуде жиі кездеседі. Хаотикалық карталар мен итерацияланған функциялар көбінесе фракталдарды жасайды. Кейбір фракталдар оларды жасайтын карталар емес, жиынтық ретінде, дербес объектілер ретінде зерттеледі. Мұның себебі көбінесе бір фракталды жасауға болатын бірнеше итерациялық процедуралардың болуы. Сондай-ақ, "Универсалдылық (динамикалық жүйелер)" тақырыбына қараңыз.
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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. 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).
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 discrete real 2 1 Euler method approximation to (non chaotic) ODE. 2D Rational chaotic map discrete rational 2 2 ACT chaotic attractor continuous real 3 Aizawa chaotic attractor continuous real 3 5 Arneodo chaotic system continuous real 3 Arnold's cat map discrete real 2 0 Baker's map discrete real 2 0 Basin chaotic map discrete real 2 1 Beta Chaotic Map 12 Bogdanov map discrete real 2 3 Brusselator continuous real 3 Burke Shaw chaotic attractor continuous real 3 2 Chen chaotic attractor continuous real 3 3 Not topologically conjugate to the Lorenz attractor. Chen Celikovsky system continuous real 3 "Generalized Lorenz canonical form of chaotic systems" Chen LU system continuous real 3 3 Interpolates between Lorenz like and Chen like behavior. Chen Lee system continuous real 3 Chossat Golubitsky symmetry map Chua circuit 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 discretecomplex 1 0 acts on the Julia set for the squaring map. Complex cubic map discrete complex 1 2 Clifford fractal map discrete real 2 4 Degenerate Double Rotor map De Jong fractal map discrete real 2 4 Delayed Logistic system discrete real 2 1 Discretized circular Van der Pol system discrete real 2 1 Euler method approximation to 'circular' Van der Pol like ODE. Discretized Van der Pol system 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 discrete real 3 Finance system continuous real 3 Folded Towel hyperchaotic map continuous real 3 Fractal Dream system discrete real 2 Gauss map discrete real 1 mouse map, Gaussian map Generalized Baker map Genesio Tesi chaotic attractor continuous real 3 Gingerbreadman map discrete real 2 0 Grinch dragon fractal discrete real 2 Gumowski/Mira map discrete real 2 1 Hadley chaotic circulation continuous real 3 0 Half inverted Rössler attractor Halvorsen chaotic attractor 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 discrete real 2 Hopalong orbit fractal discrete real 2 Hyper Logistic map discrete real 2 Hyperchaotic Chen system continuous real 3 Hyper Newton Leipnik system continuous real 4 Hyper Lorenz chaotic attractor continuous real 4 Hyper Lu chaotic system continuous real 4 Hyper Rössler chaotic attractor continuous real 4 Hyperchaotic attractor continuous real 4 Ikeda chaotic attractor 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 discrete real 2 Knot Holder chaotic oscillator continuous real 3 Kuramoto–Sivashinsky equation continuous real Lambić map discrete discrete 1 Li symmetrical toroidal chaos 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 discrete real 2 Moore Spiegel chaotic oscillator continuous real 3 Scroll Attractor continuous real 3 Jerk Circuit continuous real 3 Newton Leipnik system continuous real 3 Nordmark truncated map Nosé Hoover system continuous real 3 Novel chaotic system continuous real 3 Pickover fractal map 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 continuous real 3 3 Polynom Type B fractal map continuous real 3 6 Polynom Type C fractal map continuous real 3 18 Pulsed rotor Quadrup Two orbit fractal 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 continuous real 3 3 Rössler attractor continuous real 3 3 Rucklidge system continuous real 3 2 Sakarya chaotic attractor continuous real 3 2 Shaw Pol chaotic oscillator continuous real 3 3 Shimizu Morioka system 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 continuous real 3 2 Sprott C chaotic system continuous real 3 3 Sprott Linz A chaotic attractor continuous real 3 0 Sprott Linz B chaotic attractor continuous real 3 0 Sprott Linz C chaotic attractor continuous real 3 0 Sprott Linz D chaotic attractor continuous real 3 1 Sprott Linz E chaotic attractor continuous real 3 1 Sprott Linz F chaotic attractor continuous real 3 1 Sprott Linz G chaotic attractor continuous real 3 1 Sprott Linz H chaotic attractor continuous real 3 1 Sprott Linz I chaotic attractor continuous real 3 1 Sprott Linz J chaotic attractor continuous real 3 1 Sprott Linz K chaotic attractor continuous real 3 1 Sprott Linz L chaotic attractor continuous real 3 2 Sprott Linz M chaotic attractor continuous real 3 1 Sprott Linz N chaotic attractor continuous real 3 1 Sprott Linz O chaotic attractor continuous real 3 1 Sprott Linz P chaotic attractor continuous real 3 1 Sprott Linz Q chaotic attractor continuous real 3 2 Sprott Linz R chaotic attractor continuous real 3 2 Sprott Linz S chaotic attractor continuous real 3 1 Standard map, Kicked rotor discrete real 2 1 Chirikov standard map, Chirikov Taylor map Strizhak Kawczynski chaotic oscillator continuous real 3 9 Symmetric Flow attractor continuous real 3 1 Symplectic map Tangent map Tahn map discrete real 1 1 Ring laser map Beta distribution Thomas' cyclically symmetric attractor continuous real 3 1 Tent map discrete real 1 Tinkerbell map discrete real 2 4 Triangle map Ueda chaotic oscillator continuous real 3 3 Van der Pol oscillator continuous real 2 3 Willamowski Rössler model continuous real 3 10 WINDMI chaotic attractor continuous real 1 2 Zaslavskii map discrete real 2 4 Zaslavskii rotation map Zeraoulia Sprott map discrete real 2 2 Chialvo mapdiscretediscrete3