2 citations · 5 across the 5 of their papers we have counts for
5 papers
On the Dynamical Behaviour of Cellular Automata
Xu Xu, Yi Song, Stephen P. Banks
In this paper we study the dynamics of 1- and 2- dimensional cellular automata, using a 2-adic representation of the states, we give a simple graphical technique for finding period…
Dynamical Systems On Three Manifolds Part II: 3-Manifolds,Heegaard Splittings and Three-Dimensional Systems
Yi Song, Stephen P. Banks
The global behaviour of nonlinear systems is extremely important in control and systems theory since the usual local theories will only give information about a system in some neig…
Automorphic Forms and Reeb-Like Foliations on Three-Manifolds
Yi Song, Xu Xu, Stephen P. Banks
In this paper, we consider different ways of generating dynamical systems on 3-manifolds. We first derive explicit differential equations for dynamical systems defined on generic h…
Dynamical Systems on Three Manifolds Part I: Knots, Links and Chaos
Yi Song, S. P. Banks, David Diaz
In this paper, we give an explicit construction of dynamical systems (defined within a solid torus) containing any knot (or link) and arbitrarily knotted chaos. The first is achiev…
Inversely Unstable Solutions of Two-Dimensional Systems on Genus-p Surfaces and the Topology of Knotted Attractors
Yi Song, Stephen P. Banks
In this paper, we will show that a periodic nonlinear, time-varying dissipative system that is defined on a genus-p surface contains one or more invariant sets which act as attract…