Grenzzyklus

de

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Grenzzyklus

Quality:

Limit cycle - closed trajectory in a 2d phase space of a dynamical system such that that another trajectory spirals into it as time approaches ±∞. Article “Grenzzyklus” in German Wikipedia has 33.1 points for quality (as of July 1, 2025). The article contains 9 references and 7 sections.

This article has the best quality in Japanese Wikipedia. However, the most popular language version of this article is English.

Since the creation of article “Grenzzyklus”, its content was written by 19 registered users of German Wikipedia and edited by 222 registered Wikipedia users in all languages.

The article is cited 22 times in German Wikipedia and cited 347 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (German): #6830 in August 2012
  • Global: #73296 in May 2009

The highest popularity rank from 2008:

  • Local (German): #124173 in July 2014
  • Global: #206172 in December 2014

There are 15 language versions for this article in the WikiRank database (of the considered 55 Wikipedia language editions).

The quality and popularity assessment was based on Wikipédia dumps from July 1, 2025 (including revision history and pageviews for previous years).

The table below shows the language versions of the article with the highest quality.

Languages with the highest quality

#LanguageQuality gradeQuality score
1Japanese (ja)
リミットサイクル
45.315
2English (en)
Limit cycle
34.8399
3German (de)
Grenzzyklus
33.0945
4Catalan (ca)
Cicle límit
29.761
5Armenian (hy)
Սահմանափակ ցիկլ
23.4119
6Ukrainian (uk)
Граничний цикл
23.0926
7Chinese (zh)
极限环
19.3189
8Arabic (ar)
دورة حدودية
12.5015
9Russian (ru)
Предельный цикл
11.7357
10Persian (fa)
چرخه حدی
9.7993
More...

The following table shows the most popular language versions of the article.

Most popular in all the time

The most popular language versions of the article "Grenzzyklus" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Limit cycle
686 450
2Japanese (ja)
リミットサイクル
128 062
3Russian (ru)
Предельный цикл
75 463
4German (de)
Grenzzyklus
41 563
5Chinese (zh)
极限环
38 041
6French (fr)
Cycle limite
35 260
7Italian (it)
Ciclo limite
29 868
8Polish (pl)
Cykl graniczny
29 394
9Ukrainian (uk)
Граничний цикл
8 671
10Dutch (nl)
Limietcykel
7 094
More...

The following table shows the language versions of the article with the highest popularity in the last month.

Most popular in June 2025

The most popular language versions of the article "Grenzzyklus" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Limit cycle
2 476
2Japanese (ja)
リミットサイクル
593
3Russian (ru)
Предельный цикл
297
4Chinese (zh)
极限环
229
5French (fr)
Cycle limite
153
6German (de)
Grenzzyklus
150
7Polish (pl)
Cykl graniczny
82
8Italian (it)
Ciclo limite
71
9Persian (fa)
چرخه حدی
35
10Korean (ko)
극한 주기 궤도
34
More...

The following table shows the language versions of the article with the highest Authors’ Interest.

The highest AI

Language versions of the article "Grenzzyklus" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Limit cycle
53
2Russian (ru)
Предельный цикл
22
3French (fr)
Cycle limite
21
4Italian (it)
Ciclo limite
21
5Dutch (nl)
Limietcykel
21
6German (de)
Grenzzyklus
19
7Japanese (ja)
リミットサイクル
18
8Polish (pl)
Cykl graniczny
16
9Arabic (ar)
دورة حدودية
7
10Ukrainian (uk)
Граничний цикл
7
More...

The following table shows the language versions of the article with the highest Authors’ Interest in the last month.

The highest AI in June 2025

Language versions of the article "Grenzzyklus" with the highest AI in June 2025
#LanguageAI awardRelative AI
1French (fr)
Cycle limite
1
2Arabic (ar)
دورة حدودية
0
3Catalan (ca)
Cicle límit
0
4German (de)
Grenzzyklus
0
5English (en)
Limit cycle
0
6Persian (fa)
چرخه حدی
0
7Armenian (hy)
Սահմանափակ ցիկլ
0
8Italian (it)
Ciclo limite
0
9Japanese (ja)
リミットサイクル
0
10Korean (ko)
극한 주기 궤도
0
More...

The following table shows the language versions of the article with the highest number of citations.

The highest CI

Language versions of the article "Grenzzyklus" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1English (en)
Limit cycle
105
2Japanese (ja)
リミットサイクル
33
3Russian (ru)
Предельный цикл
30
4Chinese (zh)
极限环
29
5French (fr)
Cycle limite
28
6German (de)
Grenzzyklus
22
7Ukrainian (uk)
Граничний цикл
22
8Italian (it)
Ciclo limite
16
9Persian (fa)
چرخه حدی
13
10Polish (pl)
Cykl graniczny
12
More...

Scores

Estimated value for Wikipedia:
German:
Global:
Popularity in June 2025:
German:
Global:
Popularity in all years:
German:
Global:
Authors in June 2025:
German:
Global:
Registered authors in all years:
German:
Global:
Citations:
German:
Global:

Quality measures

Interwikis

#LanguageValue
arArabic
دورة حدودية
caCatalan
Cicle límit
deGerman
Grenzzyklus
enEnglish
Limit cycle
faPersian
چرخه حدی
frFrench
Cycle limite
hyArmenian
Սահմանափակ ցիկլ
itItalian
Ciclo limite
jaJapanese
リミットサイクル
koKorean
극한 주기 궤도
nlDutch
Limietcykel
plPolish
Cykl graniczny
ruRussian
Предельный цикл
ukUkrainian
Граничний цикл
zhChinese
极限环

Popularity rank trends

Best Rank German:
#124173
07.2014
Global:
#206172
12.2014

AI rank trends

Best Rank German:
#6830
08.2012
Global:
#73296
05.2009

Local AI rank history

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on Limit cycle from Wikipedia articles about Van der Pol oscillator, Poincaré–Bendixson theorem, Attractor, X-15 Flight 3-65-97 and Hopf bifurcation. Whereas reading the article about Limit cycle people most often go to Wikipedia articles on Van der Pol oscillator, Poincaré–Bendixson theorem, Bendixson–Dulac theorem, Attractor and Hilberts sixteenth problem.

Cumulative results of quality and popularity of the Wikipedia article

List of Wikipedia articles in different languages (starting with the most popular):

News from 10 March 2026

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In German Wikipedia the most popular articles on that day were: Cem Özdemir, Wanda Perdelwitz, Luise von Mecklenburg-Strelitz, Liste der größten Auslegerbrücken, Landtagswahl in Baden-Württemberg 2026, Dot Rotten, Guido Westerwelle, Manuel Hagel, Boris Palmer, Irankrieg 2026.

About WikiRank

The WikiRank project is intended for automatic relative evaluation of the articles in the various language versions of Wikipedia. At the moment the service allows to compare over 44 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from July, 2025. When calculating current popularity and AI of articles data from June 2025 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2025... More information