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==개요==
 
==개요==
 
* 로지스틱 맵
 
* 로지스틱 맵
−
** $x_{n+1}=ax_n (1-x_n)$ 으로 정의되는 점화식
+
** 카오스 현상을 나타내는 비선형 차분방정식의 예
 +
** <math>x_{n+1}=ax_n (1-x_n)</math> 으로 정의되는 점화식
  
  
 
==파이겐바움 분기도==
 
==파이겐바움 분기도==
 +
 +
== 노트 ==
 +
 +
===말뭉치===
 +
# However, as a demographic model the logistic map has the pathological problem that some initial conditions and parameter values (for example, if r > 4) lead to negative population sizes.<ref name="ref_30720c9d">[https://en.wikipedia.org/wiki/Logistic_map Logistic map]</ref>
 +
# The image below shows the amplitude and frequency content of some logistic map iterates for parameter values ranging from 2 to 4.<ref name="ref_30720c9d" />
 +
# In this Flong one of the most famous dynamical systems will discussed, the logistic map.<ref name="ref_1cb72f26">[https://www.complexity-explorables.org/flongs/logistic/ The Logistic Map]</ref>
 +
# The logistic map is a one-dimensional discrete-time map that, despite its formal simplicity, exhibits an unexpected degree of complexity.<ref name="ref_1cb72f26" />
 +
# It turns out that the logistic map can be motivated using a biological/ecological context.<ref name="ref_1cb72f26" />
 +
# In order to understand this behavior better, let's back up a bit and think of a system like the logistic map in more general terms.<ref name="ref_1cb72f26" />
 +
# Let’s explore an example using the famous logistic map.<ref name="ref_cf0f5058">[https://geoffboeing.com/2015/03/chaos-theory-logistic-map/ Chaos Theory and the Logistic Map]</ref>
 +
# The logistic map instead uses a nonlinear difference equation to look at discrete time steps.<ref name="ref_cf0f5058" />
 +
# Thus, each vertical slice depicts the population values that the logistic map settles toward for that parameter value.<ref name="ref_cf0f5058" />
 +
# As you adjust the growth rate parameter upwards, the logistic map will oscillate between two then four then eight then 16 then 32 (and on and on) population values.<ref name="ref_cf0f5058" />
 +
# On the other hand, if we sacrice invert- ibility temporarily, thereby introducing singularities, one-dimensional chaotic systems can easily be found, as illustrated by the celebrated logistic map.<ref name="ref_412355e2">[http://www.physics.drexel.edu/~bob/PHYS750_NLD/ch2.pdf Chapter 2]</ref>
 +
# A classical example of this is the Henon map, a dieomorphism of the plane into itself that is known to have the logistic map as a backbone.<ref name="ref_412355e2" />
 +
# As is often the case in dynamical systems theory, the action of the logistic map can not only be represented algebraically, as in Eq.<ref name="ref_412355e2" />
 +
# Given a point xn, the graph of the logistic map provides y = f (xn).<ref name="ref_412355e2" />
 +
# This so-called "logistic map" has been used as model for population dynamics, but here we just treat it as a toy model which has a transition to chaos.<ref name="ref_924eea0f">[http://physics.ucsc.edu/~peter/242/logistic.pdf The logistic map]</ref>
 +
# The logistic map computed using a graphical procedure (Tabor 1989, p. 217) is known as a web diagram.<ref name="ref_61aeac83">[https://mathworld.wolfram.com/LogisticMap.html Logistic Map -- from Wolfram MathWorld]</ref>
 +
# In order to study the fixed points of the logistic map, let an initial point lie in the interval .<ref name="ref_61aeac83" />
 +
# It is relatively easy to show that the logistic map is chaotic on an invariant Cantor set for (Devaney 1989, pp.<ref name="ref_61aeac83" />
 +
# The logistic map can be used to generate random numbers (Umeno 1998; Andrecut 1998; Gonzáles and Pino 1999, 2000; Gonzáles et al.<ref name="ref_61aeac83" />
 +
# The logistic map, whose iterations lead to period doubling and chaos as the control parameter, is increased and has three cases of the control parameter where exact solutions are known.<ref name="ref_b33839d3">[https://aip.scitation.org/doi/10.1063/1.5125097 A note on exact solutions of the logistic map]</ref>
 +
# This article presents the logistic map as a simple model suitable for introducing students to the properties of dynamical systems including periodic orbits, bifurcations, and deterministic chaos.<ref name="ref_97420f38">[https://aapt.scitation.org/doi/10.1119/1.4813114 Exploring dynamical systems and chaos using the logistic map model of population change]</ref>
 +
# The discrete logistic map is one of the most famous discrete chaotic maps which has widely spread applications.<ref name="ref_5e6ecade">[https://www.hindawi.com/journals/ddns/2015/586783/ Design of Positive, Negative, and Alternating Sign Generalized Logistic Maps]</ref>
 +
# This paper investigates a set of four generalized logistic maps where the conventional map is a special case.<ref name="ref_5e6ecade" />
 +
# Based on the maximum chaotic range of the output, the proposed maps can be classified as positive logistic map, mostly positive logistic map, negative logistic map, and mostly negative logistic map.<ref name="ref_5e6ecade" />
 +
# A systematic procedure to design two-constraint logistic map is discussed and validated through four different examples.<ref name="ref_5e6ecade" />
 +
# If you know about Chaos you probably know of the “logistic map”.<ref name="ref_b68e2112">[http://www.kierandkelly.com/what-is-chaos/logistic-map/ The Logistic Map]</ref>
 +
# The logistic map is a discrete recursive mathematical function that maps the output of one iteration of the function onto the input of the next.<ref name="ref_b68e2112" />
 +
# The logistic map models population growth & decline as a “Driven Damped System”.<ref name="ref_b68e2112" />
 +
# So just to clarify; to really understand what is going on here we need to be very clear that in the logistic map we are in fact dealing with two types of damping.<ref name="ref_b68e2112" />
 +
# The logistic map is recursive, meaning that the third term is a function of the second, the fourth a function of the third and so on.<ref name="ref_4b30d407">[http://www.physics.sfsu.edu/~mstevens/chaos/chaos.htm The Logistic Map]</ref>
 +
# In order to explore the behavior of the logistic map, I ran my C++ routine with various values for the constant m , dumped the output into an ascii file, and then graphed the output using gnu plot.<ref name="ref_4b30d407" />
 +
# Further graphs of the logistic map will continue to show this close relationship to the harmonic oscillator, and in fact a driven pendulum, a very common object, is known to show chaotic behavior.<ref name="ref_4b30d407" />
 +
# The logistic map is discussed in many references.<ref name="ref_ccbecee7">[http://www2.me.rochester.edu/courses/ME406/webexamp6/logistmap.pdf Me 406]</ref>
 +
# The other day I found some old basic code I had written about 15 years ago on a Mac Classic II to plot the Feigenbaum diagram for the logistic map.<ref name="ref_28b299a9">[https://magesblog.com/post/2012-03-17-logistic-map-feigenbaum-diagram/ Logistic map: Feigenbaum diagram in R]</ref>
 +
# For the same reason we wanted to keep the tent map inside the unit square, we keep the logistic map similarly confined.<ref name="ref_e6a1469c">[http://www.hamilton.ie/cs416/logisticmap.htm Logistic Map]</ref>
 +
# The logistic map is famous for two reasons: it gives a way of predicting how a population of animals will grow or shrink over time, and it illustrates the fascinating phenomenon of mathematical chaos.<ref name="ref_f4ea6703">[https://plus.maths.org/content/maths-minute-logistic-map Maths in a minute: The logistic map]</ref>
 +
# The logistic map takes account of the idea that the growth of the population depends on how many animals there are to start with.<ref name="ref_f4ea6703" />
 +
# It's not only the logistic map that exhibits sensitive dependence on initial conditions, but also many other mathematical expressions, such as those used to predict the weather.<ref name="ref_f4ea6703" />
 +
# What makes the logistic map special is that it's a relatively simple mathematical expression.<ref name="ref_f4ea6703" />
 +
# \(\beta \) and r of quantum logistic map is set as 6 and 3.99, respectively.<ref name="ref_5f04c96c">[https://www.nature.com/articles/s41598-020-78127-2 An image encryption scheme based on public key cryptosystem and quantum logistic map]</ref>
 +
# The time measured includes the process to generate the initial value for the underlying quantum logistic map.<ref name="ref_5f04c96c" />
 +
===소스===
 +
<references />
 +
 +
== 메타데이터 ==
 +
 +
===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q587182 Q587182]
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===Spacy 패턴 목록===
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* [{'LOWER': 'logistic'}, {'LEMMA': 'map'}]

2021년 2월 26일 (금) 02:01 기준 최신판

개요

  • 로지스틱 맵
    • 카오스 현상을 나타내는 비선형 차분방정식의 예
    • \(x_{n+1}=ax_n (1-x_n)\) 으로 정의되는 점화식


파이겐바움 분기도

노트

말뭉치

  1. However, as a demographic model the logistic map has the pathological problem that some initial conditions and parameter values (for example, if r > 4) lead to negative population sizes.[1]
  2. The image below shows the amplitude and frequency content of some logistic map iterates for parameter values ranging from 2 to 4.[1]
  3. In this Flong one of the most famous dynamical systems will discussed, the logistic map.[2]
  4. The logistic map is a one-dimensional discrete-time map that, despite its formal simplicity, exhibits an unexpected degree of complexity.[2]
  5. It turns out that the logistic map can be motivated using a biological/ecological context.[2]
  6. In order to understand this behavior better, let's back up a bit and think of a system like the logistic map in more general terms.[2]
  7. Let’s explore an example using the famous logistic map.[3]
  8. The logistic map instead uses a nonlinear difference equation to look at discrete time steps.[3]
  9. Thus, each vertical slice depicts the population values that the logistic map settles toward for that parameter value.[3]
  10. As you adjust the growth rate parameter upwards, the logistic map will oscillate between two then four then eight then 16 then 32 (and on and on) population values.[3]
  11. On the other hand, if we sacrice invert- ibility temporarily, thereby introducing singularities, one-dimensional chaotic systems can easily be found, as illustrated by the celebrated logistic map.[4]
  12. A classical example of this is the Henon map, a dieomorphism of the plane into itself that is known to have the logistic map as a backbone.[4]
  13. As is often the case in dynamical systems theory, the action of the logistic map can not only be represented algebraically, as in Eq.[4]
  14. Given a point xn, the graph of the logistic map provides y = f (xn).[4]
  15. This so-called "logistic map" has been used as model for population dynamics, but here we just treat it as a toy model which has a transition to chaos.[5]
  16. The logistic map computed using a graphical procedure (Tabor 1989, p. 217) is known as a web diagram.[6]
  17. In order to study the fixed points of the logistic map, let an initial point lie in the interval .[6]
  18. It is relatively easy to show that the logistic map is chaotic on an invariant Cantor set for (Devaney 1989, pp.[6]
  19. The logistic map can be used to generate random numbers (Umeno 1998; Andrecut 1998; Gonzáles and Pino 1999, 2000; Gonzáles et al.[6]
  20. The logistic map, whose iterations lead to period doubling and chaos as the control parameter, is increased and has three cases of the control parameter where exact solutions are known.[7]
  21. This article presents the logistic map as a simple model suitable for introducing students to the properties of dynamical systems including periodic orbits, bifurcations, and deterministic chaos.[8]
  22. The discrete logistic map is one of the most famous discrete chaotic maps which has widely spread applications.[9]
  23. This paper investigates a set of four generalized logistic maps where the conventional map is a special case.[9]
  24. Based on the maximum chaotic range of the output, the proposed maps can be classified as positive logistic map, mostly positive logistic map, negative logistic map, and mostly negative logistic map.[9]
  25. A systematic procedure to design two-constraint logistic map is discussed and validated through four different examples.[9]
  26. If you know about Chaos you probably know of the “logistic map”.[10]
  27. The logistic map is a discrete recursive mathematical function that maps the output of one iteration of the function onto the input of the next.[10]
  28. The logistic map models population growth & decline as a “Driven Damped System”.[10]
  29. So just to clarify; to really understand what is going on here we need to be very clear that in the logistic map we are in fact dealing with two types of damping.[10]
  30. The logistic map is recursive, meaning that the third term is a function of the second, the fourth a function of the third and so on.[11]
  31. In order to explore the behavior of the logistic map, I ran my C++ routine with various values for the constant m , dumped the output into an ascii file, and then graphed the output using gnu plot.[11]
  32. Further graphs of the logistic map will continue to show this close relationship to the harmonic oscillator, and in fact a driven pendulum, a very common object, is known to show chaotic behavior.[11]
  33. The logistic map is discussed in many references.[12]
  34. The other day I found some old basic code I had written about 15 years ago on a Mac Classic II to plot the Feigenbaum diagram for the logistic map.[13]
  35. For the same reason we wanted to keep the tent map inside the unit square, we keep the logistic map similarly confined.[14]
  36. The logistic map is famous for two reasons: it gives a way of predicting how a population of animals will grow or shrink over time, and it illustrates the fascinating phenomenon of mathematical chaos.[15]
  37. The logistic map takes account of the idea that the growth of the population depends on how many animals there are to start with.[15]
  38. It's not only the logistic map that exhibits sensitive dependence on initial conditions, but also many other mathematical expressions, such as those used to predict the weather.[15]
  39. What makes the logistic map special is that it's a relatively simple mathematical expression.[15]
  40. \(\beta \) and r of quantum logistic map is set as 6 and 3.99, respectively.[16]
  41. The time measured includes the process to generate the initial value for the underlying quantum logistic map.[16]

소스

  1. ↑ 1.0 1.1 Logistic map
  2. ↑ 2.0 2.1 2.2 2.3 The Logistic Map
  3. ↑ 3.0 3.1 3.2 3.3 Chaos Theory and the Logistic Map
  4. ↑ 4.0 4.1 4.2 4.3 Chapter 2
  5. ↑ The logistic map
  6. ↑ 6.0 6.1 6.2 6.3 Logistic Map -- from Wolfram MathWorld
  7. ↑ A note on exact solutions of the logistic map
  8. ↑ Exploring dynamical systems and chaos using the logistic map model of population change
  9. ↑ 9.0 9.1 9.2 9.3 Design of Positive, Negative, and Alternating Sign Generalized Logistic Maps
  10. ↑ 10.0 10.1 10.2 10.3 The Logistic Map
  11. ↑ 11.0 11.1 11.2 The Logistic Map
  12. ↑ Me 406
  13. ↑ Logistic map: Feigenbaum diagram in R
  14. ↑ Logistic Map
  15. ↑ 15.0 15.1 15.2 15.3 Maths in a minute: The logistic map
  16. ↑ 16.0 16.1 An image encryption scheme based on public key cryptosystem and quantum logistic map

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'logistic'}, {'LEMMA': 'map'}]
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