153 citations · 399 across the 15 of their papers we have counts for
16 papers
On the singularities of the discrete Korteweg-deVries equation
Doyong Um, Alfred Ramani, Basil Grammaticos +2
We study the structure of singularities in the discrete Korteweg-deVries (d-KdV) equation. Four different types of singularities are identified. The first type corresponds to local…
Rule 184 fuzzy cellular automaton as a mathematical model for traffic flow
Kohei Higashi, Junkichi Satsuma, Tetsuji Tokihiro
The rule 184 fuzzy cellular automaton is regarded as a mathematical model of traffic flow because it contains the two fundamental traffic flow models, the rule 184 cellular automat…
Revisiting the Human and Nature Dynamics model
Basil Grammaticos, Ralph Willox, Junkichi Satsuma
We present a simple model for describing the dynamics of the interaction between a homogeneous population or society, and the natural resources and reserves that the society needs…
Discrete Painlevé equations from singularity patterns: the asymmetric trihomographic case
Basil Grammaticos, Alfred Ramani, Ralph Willox +1
We derive the discrete Painlevé equations associated to the affine Weyl group E that can be represented by an (in the QRT sense) "asymmetric" trihomographic system. The m…
Calculating the algebraic entropy of mappings with unconfined singularities
Alfred Ramani, Basil Grammaticos, Ralph Willox +2
We present a method for calculating the dynamical degree of a mapping with unconfined singularities. It is based on a method introduced by Halburd for the computation of the growth…
Multiplicative equations related to the affine Weyl group E
Basil Grammaticos, Alfred Ramani, Ralph Willox +1
We derive integrable equations starting from autonomous mappings with a general form inspired by the multiplicative systems associated to the affine Weyl group E. Five su…