60 citations · 134 across the 12 of their papers we have counts for
13 papers
Analytical derivation of a three-dimensional fundamental diagram for a real-valued max-plus particle system
Daisuke Takahashi, Junta Matsukidaira, Kazuya Okamoto
We study a real-valued max-plus particle system on a finite periodic lattice. Its three-dimensional fundamental diagram relates the mean flow to two densities: the conserved partic…
Periodicity, linearizability and integrability in seed mutations of type
Atsushi Nobe, Junta Matsukidaira
In the network of seed mutations arising from a certain initial seed, an appropriate path emanating from the initial seed is intendedly chosen, noticing periodicity of the exchange…
A family of integrable and non-integrable difference equations arising from cluster algebras
Atsushi Nobe, Junta Matsukidaira
The one-parameter family of second order nonlinear difference equations each of which is given by is expl…
Max-min-plus expressions for one-dimensional particle cellular automata obtained from a fundamental diagram
Takazumi Okumura, Junta Matsukidaira, Daisuke Takahashi
We study one-dimensional neighborhood-five conservative cellular automata (CA), referred to as particle cellular automata five (particle CA5). We show that evolution equations for…
Initial value problem of evolution equations defined by lattice operators
Takatoshi Ikegami, Daisuke Takahashi, Junta Matsukidaira
We propose dynamical systems defined on algebra of lattices, which we call `lattice equations'. We give exact general solutions of initial value problems for a class of lattice equ…
Max-plus analysis on some binary particle systems
Daisuke Takahashi, Junta Matsukidaira, Hiroaki Hara +1
We concern with a special class of binary cellular automata, i.e., the so-called particle cellular automata (PCA) in the present paper. We first propose max-plus expressions to PCA…