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Dynamical Systems and Verified Numerical Computation Lab (Kaname Matsue)
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The lab explores the singular behavior of differential equations through dynamical systems theory and numerical computation.
AboutAbout the lab
Strange-looking things turn out to be simple once you change how you look at them.
The Matsue Lab studies the properties of "strange" and "singular" behavior that arises in differential equations, using dynamical systems theory and numerical analysis.
The research is grounded in applied mathematics: dynamical systems theory, differential equations, and numerical analysis (especially verified numerical computation).
The lab focuses mainly on finite-time singularities, such as solutions of differential equations blowing up in finite time, and also tackles problems that originate in combustion and energy issues.
Prof. Matsue also serves as a WPI Professor at the International Institute for Carbon-Neutral Energy Research at Kyushu University.
Key terms
- Dynamical systems
- A field of mathematics that studies how the state of a system changes over time, describing it with tools such as differential equations
- Finite-time singularity
- Singular behavior in which a solution of a differential equation blows up, goes extinct, quenches, or collides in finite time
- Verified numerical computation
- A numerical method that computes while estimating errors, so that properties such as the existence of a solution are mathematically guaranteed
NewsLab news
Prof. Matsue posted the latest preprint on arXiv and submitted it to an international journal
Prof. Matsue's paper has been accepted for publication in Oyo Suri, the journal of the Japan Society for Industrial and Applied Mathematics
A paper by Prof. Matsue and co-authors has been published in Japan Journal of Industrial and Applied Mathematics
A paper by Prof. Matsue and co-authors has been published in SIAM Journal on Applied Mathematics
A doctoral student received the Kyushu Young Mathematician Presentation Award at the Kyushu Branch Meeting of the Mathematical Society of Japan
ResearchResearch themes
Prof. Matsue's research is applied mathematics grounded in dynamical systems theory, differential equations, and numerical analysis. Its core is uncovering the fundamental properties underlying the "strange" or "singular" behavior that arises in differential equations, and it also addresses problems originating in combustion and energy issues.
*Illustrative imageFinite-Time Singularities and Dynamical Systems
The lab mainly targets finite-time singularities of solutions of differential equations, such as blow-up, extinction, quenching, and collision. It puts more effort into developing theory than into applications, centered on analyzing the behavior of ordinary differential equations at infinity (dynamics at infinity).
*Illustrative imageVerified Numerical Computation for Dynamical Systems
The lab investigates trajectories that change rapidly in finite time by using verified numerical computation. The targets are fast-slow systems, in which fast and slow motions coexist, and finite-time singularities such as blow-up solutions.
*Illustrative imagePrinciples of Flame Dynamics (Combustion Science)
The goal is to use applied mathematics to derive the guiding principles that determine how a flame moves through its interaction with physicochemical factors. The lab studies interactions between flames and the thermal expansion ratio, gravity, mass diffusion, and sound, aiming to develop highly efficient, stable, and safe combustion technologies.
MembersFaculty
- ProfessorKaname Matsue
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Flow and orbit of vector field (dynamical system)” Yapparina / CC0 (cropped)
- Finite-Time Singularities and Dynamical Systems: “The swan and the feather” Bvsydow / CC BY-SA 4.0 (cropped)
- Verified Numerical Computation for Dynamical Systems: “Jaguar Supercomputer ( )” Oak Ridge National Laboratory / CC BY 2.0 (cropped)
- Principles of Flame Dynamics (Combustion Science): “FIRE 01” MarcusObal / CC BY-SA 3.0 (cropped)
- Related lab (〈Dynamical Systems / Verified Numerical Computation〉): “FitzHugh-Nagumo Model” Cosmia Nebula / CC BY-SA 4.0 (cropped)
- Related lab (Numerical Analysis and Computational Fluid Dynamics Lab): “Biomechanics-Femur-Fracture-Nail-Internal Fixation-CAD-FEM” Fry72 Karel Frydrýšek, Tomáš Halo, Daniel Čepica / CC BY-SA 4.0 (cropped)
- Related lab (Numerical Analysis and Computational Fluid Dynamics Lab): “AbsoluteErrorNumericalDifferentiationExample” Berland / Public domain (cropped)
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