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Topic · Computer Networks and Communications

Nonlinear Dynamics and Pattern Formation

Nonlinear Dynamics and Pattern Formation is a research topic within Computer Networks and Communications. Science Explorer counts 50k research works in it since 1950. 9.9% of them reached the world's top 10% most cited for their field and year.

This cluster of papers explores the dynamics of synchronization in complex networks, focusing on phenomena such as chimera states, reaction-diffusion models, coupled oscillators, and pattern formation. The Kuramoto model and phase oscillators are central to understanding the behavior of synchronization in these systems.

  • Synchronization
  • Chimera States
  • Reaction-Diffusion Model
  • Coupled Oscillators
  • Pattern Formation
  • Network Dynamics
  • Kuramoto Model
  • Phase Oscillators
  • Complex Networks
  • Nonlinear Dynamics
Research works
50k
fractional, since 1950
In the world top 10%
4.9k
per year above
Top-10% rate
9.9%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
-1%
the tick is no change
Largest producer
China
44% of the 10 largest, 2022-now
Nonlinear Dynamics and Pattern Formation

Which countries lead Nonlinear Dynamics and Pattern Formation research?

By volume, China and the United States publish the most (2.1k and 629 works in 2022-now).

By volume, 2022-now

  1. 1 China 2.1k works
  2. 2 United States 629 works
  3. 3 India 463 works
  4. 4 Russia 370 works
  5. 5 Germany 253 works
  6. 6 Japan 251 works
  7. 7 France 224 works
  8. 8 United Kingdom 200 works
  9. 9 Italy 155 works
  10. 10 Brazil 126 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 43.9%United States: 13.2%India: 9.7%Russia: 7.8%6 others listed: 25.4%44%largest
China2,087 · 43.9%United States629 · 13.2%India463 · 9.7%Russia370 · 7.8%6 others listed1,209 · 25.4%

Shares of the rows listed above, not of the whole node.

Which institutions lead Nonlinear Dynamics and Pattern Formation research?

By volume in 2022-now, Russian Academy of Sciences publishes the most Nonlinear Dynamics and Pattern Formation research, followed by Centre National de la Recherche Scientifique and Harbin Institute of Technology.

By volume, 2022-now

  1. 1 Russian Academy of SciencesRussia 114 works
  2. 2 Centre National de la Recherche ScientifiqueFrance 102 works
  3. 3 Harbin Institute of TechnologyChina 48 works
  4. 4 Chinese Academy of SciencesChina 38 works
  5. 5 Southeast UniversityChina 35 works
  6. 6 Yaroslavl State UniversityRussia 35 works
  7. 7 Jiangsu UniversityChina 32 works
  8. 8 Max Planck SocietyGermany 30 works
  9. 9 Northeastern UniversityChina 27 works
  10. 10 The University of TokyoJapan 23 works

Who are the leading researchers in Nonlinear Dynamics and Pattern Formation?

The most-cited researchers publishing on Nonlinear Dynamics and Pattern Formation include Karl John Friston, Róbert Langer and George M. Whitesides.

  1. 1 Karl John Friston United Kingdom 310k citations
  2. 2 Róbert Langer United States 303k citations
  3. 3 George M. Whitesides United States 267k citations
  4. 4 Donald G. Truhlar United States 230k citations
  5. 5 Kai You Wang China 224k citations
  6. 6 Albert-Ĺaszló Barabási United States 223k citations
  7. 7 Frede Blaabjerg Denmark 203k citations
  8. 8 Harry Eugene Stanley United States 198k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Nonlinear Dynamics and Pattern Formation?

The most cited paper in Nonlinear Dynamics and Pattern Formation is "Collective dynamics of ‘small-world’ networks" (Duncan J. Watts, Steven H. Strogatz, 1998), with 43,707 citations. Next come "Complex networks: Structure and dynamics" (11,156) and "Synchronization in chaotic systems" (10,638).

Most cited papers
#PaperReleasedCitations
1 Collective dynamics of ‘small-world’ networks Duncan J. Watts, Steven H. Strogatz · Nature Jun 1998 43,707
2 Complex networks: Structure and dynamics Stefano Boccaletti, Vito Latora, Yamir Moreno et al. · Physics Reports 11 Jan 2006 11,156
3 Synchronization in chaotic systems Louis M. Pecora, Thomas L. Carroll · Physical Review Letters 19 Feb 1990 10,638
4 Determining Lyapunov exponents from a time series Alan Wolf, Jack B. Swift, Harry L. Swinney et al. · Physica D Nonlinear Phenomena Open access Jul 1985 9,535
5 Exploring complex networks Steven H. Strogatz · Nature Mar 2001 8,412
All 99 most cited papers, with filters and sorting

Where is Nonlinear Dynamics and Pattern Formation research done?

The largest centres of Nonlinear Dynamics and Pattern Formation research in 2022-now are Beijing (China), Nanjing (China), Shanghai (China) and Moscow (Russia). Among places with at least 20 works in it, it is an unusually large share of all research in Yaroslavl and Saratov.

Largest cities, 2022-now

  1. 1 BeijingChina 206 works
  2. 2 NanjingChina 139 works
  3. 3 ShanghaiChina 138 works
  4. 4 MoscowRussia 110 works
  5. 5 Xi'anChina 104 works
  6. 6 WuhanChina 93 works
  7. 7 HarbinChina 91 works
  8. 8 TokyoJapan 85 works
  9. 9 ChengduChina 72 works
  10. 10 GuangzhouChina 70 works

Where it is the local speciality

  1. YaroslavlRU · 35.2 works39×
  2. SaratovRU · 24.1 works17×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Nonlinear Dynamics and Pattern Formation than the world average.

See Nonlinear Dynamics and Pattern Formation on the map

Where is the best place to study Nonlinear Dynamics and Pattern Formation?

Among universities, judged by research, Central China Normal University, Southeast University and Indian Statistical Institute score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%60%mean 26.66%fractional works in this field (log) →share of work in the world top 10% →Indian Statistical I…Central China Normal…Southeast UniversityXinjiang University
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Central China Normal UniversityChina 72.749.0%13.5×19 +240.5%
2Southeast UniversityChina 69.728.2%4.4×36 +17.5%
3Indian Statistical InstituteIndia 64.056.6%26.5×12 -2.1%
4Xinjiang UniversityChina 61.025.6%9.4×22 +39.2%
5Harbin Institute of TechnologyChina 56.618.8%5.4×48 -14.8%
6Jiangsu UniversityChina 54.612.6%7.4×32 +42.0%
7Northeastern UniversityChina 46.913.5%5.5×27 +4.5%
8Tongji UniversityChina 46.017.3%2.3×19 +53.2%
9Yanshan UniversityChina 45.722.5%7.2×14 +16.3%
10City University of Hong KongChina 45.122.5%3.7×12 -14.7%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Nonlinear Dynamics and Pattern Formation, country by country

Is Nonlinear Dynamics and Pattern Formation research growing?

Output in 2022-2025 was 1% lower than in 2018-2021, peaking in 2013.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Nonlinear Dynamics and Pattern Formation as a percentage of every work published that year, 0.025% in 2024.

still counting0.050%0.10%Nonlinear Dynamics and Pattern Formation0.024% in 202519801990200020102020

Fractional works of Nonlinear Dynamics and Pattern Formation over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Nonlinear Dynamics and Pattern Formation9.8% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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