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Advanced Differential Equations and Dynamical Systems

Advanced Differential Equations and Dynamical Systems is a research topic within Geometry and Topology. Science Explorer counts 24k research works in it since 1950. 11.9% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the study of bifurcations in planar polynomial systems, particularly emphasizing piecewise linear structures, limit cycles, Hopf bifurcations, discontinuous systems, nilpotent singularities, Darboux integrability, and Abelian integrals.

  • Bifurcations
  • Planar Systems
  • Piecewise Linear
  • Limit Cycles
  • Polynomial Vector Fields
  • Hopf Bifurcation
  • Discontinuous Systems
  • Nilpotent Singularity
  • Darboux Integrability
  • Abelian Integrals
Research works
24k
fractional, since 1950
In the world top 10%
2.8k
per year above
Top-10% rate
11.9%
share of its works in the world top 10%
Growth, 2013–17 → 2018–22
+1%
the tick is no change

Which countries lead Advanced Differential Equations and Dynamical Systems research?

By volume, China and the United States publish the most (598 and 242 works in 2022–2025).

By volume, 2022–2025

  1. 1 China 598 works
  2. 2 United States 242 works
  3. 3 Russia 202 works
  4. 4 India 164 works
  5. 5 Spain 139 works
  6. 6 Brazil 133 works
  7. 7 France 130 works
  8. 8 Germany 83 works
  9. 9 Japan 77 works
  10. 10 Italy 66 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: 32.6%United States: 13.2%Russia: 11.0%India: 9.0%6 others listed: 34.2%33%largest
China598 · 32.6%United States242 · 13.2%Russia202 · 11.0%India164 · 9.0%6 others listed628 · 34.2%

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

Which institutions lead Advanced Differential Equations and Dynamical Systems research?

By volume in 2022–2025, Universitat Autònoma de Barcelona publishes the most Advanced Differential Equations and Dynamical Systems research, followed by National Research University Higher School of Economics and Southern Illinois University Edwardsville.

Who are the leading researchers in Advanced Differential Equations and Dynamical Systems?

The most-cited researchers publishing on Advanced Differential Equations and Dynamical Systems include Guanrong Chen, Jinde Cao and Leon O. Chua.

  1. 1 Guanrong Chen Hong Kong 5.4k citations
  2. 2 Jinde Cao China 4.2k citations
  3. 3 Leon O. Chua United States 4.1k citations
  4. 4 Shankar Sastry United States 2.5k citations

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

Where is Advanced Differential Equations and Dynamical Systems research done?

The largest centres of Advanced Differential Equations and Dynamical Systems research in 2022–2025 are Moscow (Russia), Beijing (China), Shanghai (China) and Cerdanyola del Vallès (Spain). Among places with at least 20 works in it, it is an unusually large share of all research in Edwardsville and Cerdanyola del Vallès.

Largest cities, 2022–2025

  1. 1 Moscow Russia 110 works
  2. 2 Beijing China 79 works
  3. 3 Shanghai China 47 works
  4. 4 Cerdanyola del Vallès Spain 47 works
  5. 5 Paris France 41 works
  6. 6 Guangzhou China 40 works
  7. 7 Chengdu China 36 works
  8. 8 Changsha China 29 works
  9. 9 Tokyo Japan 28 works
  10. 10 São Paulo Brazil 28 works

Where it is the local speciality

  1. EdwardsvilleUS · 20.3 works175×
  2. Cerdanyola del VallèsES · 46.5 works38×
← less than its size predictsmore →

Location quotient: how much more of its research is in Advanced Differential Equations and Dynamical Systems than the world average.

See Advanced Differential Equations and Dynamical Systems on the map

Where is the best place to study Advanced Differential Equations and Dynamical Systems?

Among universities, judged by research, Sidi Mohamed Ben Abdellah University, Universitat Autònoma de Barcelona and Zhejiang Normal University 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%mean 23.19%fractional works in this node (log) →share in the world top 10% →Sidi Mohamed Ben Abdellah University: 9, 47.2%Universitat Autònoma de Barcelona: 46, 15.4%Zhejiang Normal University: 15, 35.1%University Mohamed El Bachir El Ibrahimi of Bordj Bou Arreridj: 16, 17.2%Lomonosov Moscow State University: 20, 9.4%Universidade Estadual de Campinas (UNICAMP): 14, 28.3%National Research University Higher School of Economics: 21, 4.4%Universitat de Lleida: 8, 26.0%Sichuan University: 18, 38.6%University of Lisbon: 13, 10.3%Sidi Mohamed Ben Abd…Zhejiang Normal Univ…University Mohamed E…Universitat Autònoma…
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1 Sidi Mohamed Ben Abdellah UniversityMorocco 64.447.2%12.3×9
2 Universitat Autònoma de BarcelonaSpain 63.315.4%41.2×46 -4.9%
3 Zhejiang Normal UniversityChina 57.535.1%19.2×15 -57.8%
4 University Mohamed El Bachir El Ibrahimi of Bordj Bou ArreridjAlgeria 55.817.2%275.5×16
5 Lomonosov Moscow State UniversityRussia 49.99.4%8.8×20 +35.1%
6 Universidade Estadual de Campinas (UNICAMP)Brazil 49.328.3%6.9×14 +65.3%
7 National Research University Higher School of EconomicsRussia 47.74.4%19.5×21 +51.1%
8 Universitat de LleidaSpain 47.626.0%33.1×8 -18.2%
9 Sichuan UniversityChina 44.838.6%4.0×18 +7.0%
10 University of LisbonPortugal 44.210.3%8.0×13 +59.9%

Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.

Is Advanced Differential Equations and Dynamical Systems research growing?

Output in 2018–2022 was 1% higher than in 2013–2017, peaking in 2011. The fastest-growing topics are Advanced Differential Equations and Dynamical Systems.

19801990200020102020
grewheldshrank

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

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.