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).
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.
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.
By volume, 2022–2025
- 1 Universitat Autònoma de BarcelonaSpain 47 works
- 2 National Research University Higher School of EconomicsRussia 21 works
- 3 Southern Illinois University EdwardsvilleUnited States 20 works
- 4 Centre National de la Recherche ScientifiqueFrance 20 works
- 5 Lomonosov Moscow State UniversityRussia 20 works
- 6 Sichuan UniversityChina 18 works
- 7 Universidade Estadual Paulista (Unesp)Brazil 17 works
- 8 University Mohamed El Bachir El Ibrahimi of Bordj Bou ArreridjAlgeria 16 works
- 9 Sun Yat-sen UniversityChina 15 works
- 10 Shanghai Jiao Tong UniversityChina 15 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 Guanrong Chen, Jinde Cao and Leon O. Chua.
- 1 Guanrong Chen Hong Kong 5.4k citations
- 2 Jinde Cao China 4.2k citations
- 3 Leon O. Chua United States 4.1k citations
- 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
Where it is the local speciality
- EdwardsvilleUS · 20.3 works175×
- Cerdanyola del VallèsES · 46.5 works38×
Location quotient: how much more of its research is in Advanced Differential Equations and Dynamical Systems than the world average.
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.
One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.
| # | University | Score | Top 10% | Specialisation | Works | Growth |
|---|---|---|---|---|---|---|
| 1 | Sidi Mohamed Ben Abdellah UniversityMorocco | 64.4 | 47.2% | 12.3× | 9 | — |
| 2 | Universitat Autònoma de BarcelonaSpain | 63.3 | 15.4% | 41.2× | 46 | -4.9% |
| 3 | Zhejiang Normal UniversityChina | 57.5 | 35.1% | 19.2× | 15 | -57.8% |
| 4 | University Mohamed El Bachir El Ibrahimi of Bordj Bou ArreridjAlgeria | 55.8 | 17.2% | 275.5× | 16 | — |
| 5 | Lomonosov Moscow State UniversityRussia | 49.9 | 9.4% | 8.8× | 20 | +35.1% |
| 6 | Universidade Estadual de Campinas (UNICAMP)Brazil | 49.3 | 28.3% | 6.9× | 14 | +65.3% |
| 7 | National Research University Higher School of EconomicsRussia | 47.7 | 4.4% | 19.5× | 21 | +51.1% |
| 8 | Universitat de LleidaSpain | 47.6 | 26.0% | 33.1× | 8 | -18.2% |
| 9 | Sichuan UniversityChina | 44.8 | 38.6% | 4.0× | 18 | +7.0% |
| 10 | University of LisbonPortugal | 44.2 | 10.3% | 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.
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.