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Topic · Geometry and Topology

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. 10.2% 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%
2.4k
per year above
Top-10% rate
10.2%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+5%
the tick is no change
Largest producer
China
33% of the 10 largest, 2022-now
Advanced Differential Equations and Dynamical Systems

Which countries lead Advanced Differential Equations and Dynamical Systems research?

By volume, China and the United States publish the most (660 and 267 works in 2022-now).

By volume, 2022-now

  1. 1 China 660 works
  2. 2 United States 267 works
  3. 3 Russia 217 works
  4. 4 India 176 works
  5. 5 Spain 151 works
  6. 6 Brazil 150 works
  7. 7 France 141 works
  8. 8 Germany 91 works
  9. 9 Japan 86 works
  10. 10 Algeria 72 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: 32.8%United States: 13.3%Russia: 10.8%India: 8.7%6 others listed: 34.4%33%largest
China660 · 32.8%United States267 · 13.3%Russia217 · 10.8%India176 · 8.7%6 others listed691 · 34.4%

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-now, Centre National de la Recherche Scientifique publishes the most Advanced Differential Equations and Dynamical Systems research, followed by Russian Academy of Sciences and Universitat Autònoma de Barcelona.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 72 works
  2. 2 Russian Academy of SciencesRussia 69 works
  3. 3 Universitat Autònoma de BarcelonaSpain 61 works
  4. 4 National Research University Higher School of EconomicsRussia 22 works
  5. 5 Southern Illinois University EdwardsvilleUnited States 22 works
  6. 6 Lomonosov Moscow State UniversityRussia 21 works
  7. 7 Universidade Estadual Paulista (Unesp)Brazil 19 works
  8. 8 Sichuan UniversityChina 19 works
  9. 9 Sun Yat-sen UniversityChina 17 works
  10. 10 University Mohamed El Bachir El Ibrahimi of Bordj Bou ArreridjAlgeria 17 works

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 Tasawar Hayat, Hywel C Williams and Xiang Zhang.

  1. 1 Tasawar Hayat Pakistan 135k citations
  2. 2 Hywel C Williams United Kingdom 126k citations
  3. 3 Xiang Zhang United States 119k 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 Advanced Differential Equations and Dynamical Systems?

The most cited paper in Advanced Differential Equations and Dynamical Systems is "Basic problems in stability and design of switched systems" (Daniel Liberzon, A. Stephen Morse, 1999), with 3,641 citations. Next come "Quantitative universality for a class of nonlinear transformations" (3,615) and "Multiple Lyapunov functions and other analysis tools for switched and hybrid systems" (3,292).

Most cited papers
#PaperReleasedCitations
1 Basic problems in stability and design of switched systems Daniel Liberzon, A. Stephen Morse · IEEE Control Systems Oct 1999 3,641
2 Quantitative universality for a class of nonlinear transformations Mitchell J. Feigenbaum · Journal of Statistical Physics Jul 1978 3,615
3 Multiple Lyapunov functions and other analysis tools for switched and hybrid systems Michael S. Branicky · IEEE Transactions on Automatic Control Apr 1998 3,292
4 A two-dimensional mapping with a strange attractor M. Hénon · Communications in Mathematical Physics Feb 1976 3,002
5 Doctoral Dissertation Michael Monastyrsky · Birkhäuser Boston eBooks Book chapter 1987 2,609
All 100 most cited papers, with filters and sorting

Where is Advanced Differential Equations and Dynamical Systems research done?

The largest centres of Advanced Differential Equations and Dynamical Systems research in 2022-now are Moscow (Russia), Beijing (China), Cerdanyola del Vallès (Spain) and Shanghai (China). 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-now

  1. 1 MoscowRussia 116 works
  2. 2 BeijingChina 85 works
  3. 3 Cerdanyola del VallèsSpain 52 works
  4. 4 ShanghaiChina 50 works
  5. 5 GuangzhouChina 44 works
  6. 6 ParisFrance 44 works
  7. 7 ChengduChina 38 works
  8. 8 ChangshaChina 32 works
  9. 9 São PauloBrazil 31 works
  10. 10 TokyoJapan 30 works

Where it is the local speciality

  1. EdwardsvilleUS · 21.7 works161×
  2. Cerdanyola del VallèsES · 51.7 works38×
← less than its size predicts1×more →

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, Zhejiang Normal University, Universitat Autònoma de Barcelona and Sidi Mohamed Ben Abdellah 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 19.43%fractional works in this field (log) →share of work in the world top 10% →Zhejiang Normal Univ…Sidi Mohamed Ben Abd…Universidade Estadua…Universitat Autònoma…
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
1Zhejiang Normal UniversityChina 70.837.2%21.7×16 +51.7%
2Universitat Autònoma de BarcelonaSpain 63.56.7%36.7×61 -7.5%
3Sidi Mohamed Ben Abdellah UniversityMorocco 63.532.2%13.4×9 +72.5%
4Universidade Estadual de Campinas (UNICAMP)Brazil 55.720.0%7.9×15 +11.8%
5Universidad de SevillaSpain 48.221.5%6.0×9 +19.1%
6Sichuan UniversityChina 44.616.3%3.2×19 +80.4%
7Central South UniversityChina 44.619.1%2.9×14 +91.1%
8Universidade Estadual Paulista (Unesp)Brazil 44.45.9%9.1×19 +61.8%
9Universidade Federal de GoiásBrazil 42.213.0%10.4×9 +24.3%
10Shanghai Jiao Tong UniversityChina 41.822.4%2.2×16 -28.5%

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 Advanced Differential Equations and Dynamical Systems, country by country

Is Advanced Differential Equations and Dynamical Systems research growing?

Output in 2022-2025 was 5% higher than in 2018-2021, peaking in 2011. The fastest-growing topics are Advanced Differential Equations and Dynamical Systems.

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 Advanced Differential Equations and Dynamical Systems as a percentage of every work published that year, 0.013% in 2024.

still counting0.020%0.040%0.060%Advanced Differential Equations and Dynamical Systems0.011% in 202519801990200020102020

Fractional works of Advanced Differential Equations and Dynamical Systems 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%Advanced Differential Equations and Dynamical Systems10.4% 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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