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Mathematics of Dynamical Systems Lab
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A butterfly's wingbeat can change the weather, and this lab uses mathematics to unravel chaos and bifurcation.
AboutAbout the lab
Tiny differences that change the future
The Mathematics of Dynamical Systems Lab studies the theory of dynamical systems, which covers all kinds of mathematical models that change over time.
Its goal is to uncover complex phenomena such as chaos and bifurcation that occur in various systems in the natural sciences and engineering, and to create new engineering technologies.
The lab takes on the development of new dynamical systems theories that go beyond conventional theory, and also uses verified numerical computation and large-scale numerical simulation.
Key terms
- Dynamical system
- A general term for mathematical models whose state changes over time, and the field of mathematics that studies them
- Chaos
- Behavior in which, even though a system follows fixed rules, a slight difference in the initial state leads to greatly different outcomes, making prediction difficult
- Bifurcation
- A phenomenon in which a small change in a parameter causes the behavior of a system to change dramatically
ResearchResearch themes
Using methods from dynamical systems theory, the lab aims to clarify complex phenomena such as chaos and bifurcation that appear in various systems in the natural sciences and engineering, and to create new engineering technologies.
*Illustrative imageThe structure of bifurcations in various equations
The lab develops theories of bifurcation phenomena in various systems of differential equations, including Hamiltonian systems, reversible systems, piecewise smooth systems, and stochastic dynamical systems, and clarifies their structure. It also studies solutions of the four-body problem in classical mechanics.
*Illustrative imageCollective behavior of many particles
Rather than tracking particles one by one, the lab describes a large number of particles by their distribution and studies how the group changes over time. This reveals, for example, phase transitions in nonequilibrium states and how the time needed to settle into thermal equilibrium depends on the number of particles.
*Illustrative imageApplications to rocket trajectories and infectious diseases
Building on dynamical systems theory, the lab develops data science methods. It also works on clarifying how infectious diseases spread, designing low-cost trajectories for space rockets, and motion control of drones.
MembersFaculty
The Mathematics of Dynamical Systems Lab consists of faculty members, researchers, doctoral students, master's students, and fourth-year undergraduates.
- Associate ProfessorMitsuru Shibayama
- Assistant ProfessorYoshiyuki Yamaguchi
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: “PIA21427 - TRAPPIST-1 Planetary Orbits and Transits (screenshot)” NASA/JPL-Caltech / Public domain (cropped)
- The structure of bifurcations in various equations: “Logistic Map Bifurcation Diagram, Matplotlib, zoomed” Morn / CC BY-SA 4.0 (cropped)
- Collective behavior of many particles: “Parc du réservoir Beaudet” Wilfredor / CC0 (cropped)
- Applications to rocket trajectories and infectious diseases: “Lucy spacecraft trajectory” NASA / Public domain (cropped)
- Related lab (Nonlinear Dynamics and Computational Physics Group): “Mandel zoom 11 satellite double spiral” Created by Wolfgang Beyer with the program Ultra Fractal 3. / CC BY-SA 3.0 (cropped)
- Related lab (Theoretical Neuroscience and Mathematics of Nonequilibrium Systems Group): “Neuron Heart” Piku4chemia / CC BY-SA 4.0 (cropped)
- Related lab (Physical Statistics Lab): “Chaos Theory & Double Pendulum - 3” Cristian V. / CC BY-SA 4.0 (cropped)
- Related lab (Collective Intelligence Systems Lab): “DataAppliedWeb” Marksenizer / CC BY-SA 3.0 (cropped)
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