4 papers
Low-Dimensional Reduction of Mean-Field Coupled Dynamical Systems with Units Described by Two Real Variables: Classification and Applications
Kai Tokunaga
Low-dimensional reduction is crucial for understanding network systems with many units. In a recent advance, Martens and Dharmavaram developed a theory of exact low-dimensional red…
Low-Dimensional Reduction Theory for Populations of Phase Oscillators with a Gaussian Frequency Distribution
Kai Tokunaga
Low-dimensional reduction theories such as the Ott-Antonsen ansatz have played a crucial role in the study of populations of coupled oscillators. Their application, however, has la…
Exact Low-Dimensional Reduction Theory for Populations of Stuart--Landau Oscillators
Kai Tokunaga
This paper develops an exact low-dimensional reduction theory for populations of Stuart-Landau oscillators. The theory covers two cases: in one case, coupling enters only through t…
Low-Dimensional Reduction Theory for Populations of Globally Coupled Phase Oscillators with Multiharmonic Coupling: A Method Based on OPUC Theory
Kai Tokunaga
Low-dimensional reduction theories such as the Ott-Antonsen ansatz have played a crucial role in the study of populations of coupled oscillators. However, most of these theories ap…