Hopf bifurcation

en

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Hopf bifurcation

Quality:

Hopf bifurcation - critical point where a periodic solution arises. Article “Hopf bifurcation” in English Wikipedia has 58.7 points for quality (as of July 1, 2025). The article contains 16 references and 18 sections.

In this language version of Wikipedia the article has the best quality. Also, this article is the most popular in that (English) language version.

Since the creation of article “Hopf bifurcation”, its content was written by 67 registered users of English Wikipedia and edited by 172 registered Wikipedia users in all languages.

The article is cited 45 times in English Wikipedia and cited 167 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (English): #40122 in January 2006
  • Global: #58023 in January 2020

The highest popularity rank from 2008:

  • Local (English): #178317 in December 2011
  • Global: #146411 in December 2014

There are 10 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
1English (en)
Hopf bifurcation
58.6716
2French (fr)
Bifurcation de Hopf
20.7728
3German (de)
Hopf-Bifurkation
15.7229
4Chinese (zh)
霍普夫分岔
14.8221
5Italian (it)
Biforcazione di Hopf
7.1902
6Russian (ru)
Бифуркация Андронова — Хопфа
6.1025
7Ukrainian (uk)
Біфуркація Андронова — Гопфа
5.7194
8Dutch (nl)
Hopf-bifurcatie
5.4378
9Japanese (ja)
ホップ分岐
5.1244
10Korean (ko)
호프 분기
0.0944
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 "Hopf bifurcation" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Hopf bifurcation
711 755
2Japanese (ja)
ホップ分岐
87 019
3German (de)
Hopf-Bifurkation
65 686
4Russian (ru)
Бифуркация Андронова — Хопфа
43 444
5Italian (it)
Biforcazione di Hopf
29 886
6French (fr)
Bifurcation de Hopf
28 193
7Chinese (zh)
霍普夫分岔
13 513
8Dutch (nl)
Hopf-bifurcatie
11 552
9Ukrainian (uk)
Біфуркація Андронова — Гопфа
6 925
10Korean (ko)
호프 분기
408
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 "Hopf bifurcation" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Hopf bifurcation
3 138
2Russian (ru)
Бифуркация Андронова — Хопфа
277
3German (de)
Hopf-Bifurkation
272
4Japanese (ja)
ホップ分岐
212
5French (fr)
Bifurcation de Hopf
192
6Chinese (zh)
霍普夫分岔
154
7Italian (it)
Biforcazione di Hopf
119
8Dutch (nl)
Hopf-bifurcatie
30
9Korean (ko)
호프 분기
14
10Ukrainian (uk)
Біфуркація Андронова — Гопфа
14
More...

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

The highest AI

Language versions of the article "Hopf bifurcation" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Hopf bifurcation
67
2German (de)
Hopf-Bifurkation
26
3Dutch (nl)
Hopf-bifurcatie
17
4French (fr)
Bifurcation de Hopf
12
5Russian (ru)
Бифуркация Андронова — Хопфа
11
6Italian (it)
Biforcazione di Hopf
10
7Japanese (ja)
ホップ分岐
10
8Ukrainian (uk)
Біфуркація Андронова — Гопфа
10
9Chinese (zh)
霍普夫分岔
8
10Korean (ko)
호프 분기
1
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 "Hopf bifurcation" with the highest AI in June 2025
#LanguageAI awardRelative AI
1Russian (ru)
Бифуркация Андронова — Хопфа
1
2German (de)
Hopf-Bifurkation
0
3English (en)
Hopf bifurcation
0
4French (fr)
Bifurcation de Hopf
0
5Italian (it)
Biforcazione di Hopf
0
6Japanese (ja)
ホップ分岐
0
7Korean (ko)
호프 분기
0
8Dutch (nl)
Hopf-bifurcatie
0
9Ukrainian (uk)
Біфуркація Андронова — Гопфа
0
10Chinese (zh)
霍普夫分岔
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 "Hopf bifurcation" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1Italian (it)
Biforcazione di Hopf
47
2English (en)
Hopf bifurcation
45
3German (de)
Hopf-Bifurkation
21
4Dutch (nl)
Hopf-bifurcatie
12
5French (fr)
Bifurcation de Hopf
8
6Japanese (ja)
ホップ分岐
8
7Russian (ru)
Бифуркация Андронова — Хопфа
8
8Ukrainian (uk)
Біфуркація Андронова — Гопфа
8
9Chinese (zh)
霍普夫分岔
7
10Korean (ko)
호프 분기
3
More...

Scores

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

Quality measures

Interwikis

#LanguageValue
deGerman
Hopf-Bifurkation
enEnglish
Hopf bifurcation
frFrench
Bifurcation de Hopf
itItalian
Biforcazione di Hopf
jaJapanese
ホップ分岐
koKorean
호프 분기
nlDutch
Hopf-bifurcatie
ruRussian
Бифуркация Андронова — Хопфа
ukUkrainian
Біфуркація Андронова — Гопфа
zhChinese
霍普夫分岔

Popularity rank trends

Best Rank English:
#178317
12.2011
Global:
#146411
12.2014

AI rank trends

Best Rank English:
#40122
01.2006
Global:
#58023
01.2020

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on Hopf bifurcation from Wikipedia articles about Bifurcation theory, Pitchfork bifurcation, Saddle-node bifurcation, Van der Pol oscillator and Lorenz system. Whereas reading the article about Hopf bifurcation people most often go to Wikipedia articles on Bifurcation theory, Eberhard Hopf, Limit cycle, Reaction–diffusion system and Pitchfork bifurcation.

Cumulative results of quality and popularity of the Wikipedia article

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

News from 16 March 2026

On 16 March 2026 in multilingual Wikipedia, Internet users most often read articles on the following topics: 98th Academy Awards, Michael B. Jordan, Sinners, Jessie Buckley, Paul Thomas Anderson, Sean Penn, One Battle After Another, Amy Madigan, Hamnet, Timothée Chalamet.

In English Wikipedia the most popular articles on that day were: 98th Academy Awards, Michael B. Jordan, Paul Thomas Anderson, Jessie Buckley, Sinners (2025 film), Amy Madigan, Autumn Durald Arkapaw, Maya Rudolph, Sean Penn, Academy Awards.

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